Particulars VIP Middle Last = = % of 60 = 30

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2 Ans. 1: 1. Basic Computations Less: Less: Gross Seats Free Seats Net Saleable Seats Particulars VIP Middle Last Firm Booking by Troupe 3 3 = = 3 6 5% of 6 = = 36 Nil 36 5% of 36 = = 18 Nil 18 5% of 18 = 9 Seats available for sale by Entertain U Net Contribution per person ` 32 ` 2 = ` 3 ` 22 ` 2 = ` 2 ` 12 ` 2 = ` 1 Contribution earned from Firm Booking 3 ` 3 = ` 9, 18 ` 2= ` 36, 9 ` 1= ` 9, ` 54, 2. Fixed Costs to be recovered for BEP (a) Drama Troupe Hire (b) Rent for the Theatre (c) Air Conditioning and other Stage Arrangement Charges (d) Food for VIP Free Guests (not charged) = 3 persons ` 2 ` 71, ` 14, ` 7,4 ` 6 ` 93, Less: Recovery by way of Sponsor ` 9, Contribution from Firm Booking (WN 1) ` 54, ` 63, Net Fixed Costs to be recovered ` 3, 3. BEP at different seats mix Particulars VIP Middle Last Total (a) Contribution per person ` 3 ` 2 ` 1 (b) Given Demand Ratio (c) Overall Contribution Ratio (a b) (d) Apportionment of ` 3, (WN 2) ` 9, ` 18, ` 3, `3, as per above ratio (e) BEP Number of Seats (d a) This is compared with WN 1 Seats available for sale by Entertain U, and found feasible. Hence, it is a valid BEP. (f) Revised Demand Ratio (g) Revised Overall Contribution Ratio (a f) (h) Apportionment of ` 3, (WN 2) ` 12, ` 8, ` 1, `3, as per revised ratio (i) Required BEP Number of Seats (h a) (j) Seats available for sale by Entertain U (WN 1) (k) Balance seats not available for sale (i j) 1 NA 1 (l) Contribution lost on above seats (a k) ` 3, ` 1, ` 4, (m) Additional Seats to make good above Contribution Lost = 4 2 (n) Revised BEP (however not in 2 : 2 : 5 Ratio) 3 4+2=6 9 18

3 Ans. 2: 1. Computation of BEQ with Present Mix of 3 : 2 Particulars E Z Total (a) Contribution per unit ` 25 ` 2 (b) Sales Mix Ratio 3 2 (c) Overall Contribution Ratio (a X b) (d) To achieve BEQ, Required Contribution = Fixed Cost of ` 46, to ` 3, ` 16, ` 46, be earned in the ratio of 75 : 4 (e) Hence, Required BEQ = (d a) 1,2 units 8 units 2, units 2. Statement of Product Ranking at different sale quantity levels Particulars Product E Product Z Sale Quantity (units) Upto Upto Contribution pu (`) Ranking I II III II III IV 3. Minimum Addnl Quantity to recover Additional Fixed Costs (as per ranking preference in Working Note 2) (a) Additional Fixed Cost to be recovered 47,5 (b) I Rank: Additional 1, units of E with Contribution of ` 25 per unit. (25 1) (25,) (c) Balance Fixed Costs to be Recovered (a b) 22,5 (d) II Rank: Additional 1, units of either E or Z with Contribution of ` 2 p.u. (2 1) (2,) (e) Balance Fixed Costs to be Recovered (c d) 2,5 (f) II Rank: Additional units of either E or Z (as per previous decision) with Contribution of ` 2 p.u. Note: Number of units to be sold = ` 2,5 ` 2 p.u = 125 units (25) Number of Units from which All Fixed Costs are recovered is as under Particulars E Z Option I Given 3, + WN 3(b) 1, + WN 3(d) 1, = 5, units Option II Given 3, + WN 3(b) 1, + WN 3(f) 125 = 4,125 units 4. Computation of Optimum Product Mix, etc. (a) Total Quantity to be sold = 5, units + 4 units = (b) From the Ranking Table, the Optimum Combination will be (in units) Given 2, + WN 3(f) 125 = 2,125 units Given 2, + WN 3(d) 1, = 3, units 9, units E = 5, & Z = 4, uts (c) Total Contribution: E (4, units X ` 25) + (1, units X ` 2) = 1,2, Z (4, units X ` 2) 8, ` 2,, (d) Total Average Contribution per unit = (2,, 9, units) ` per unit (e) Total Profits = Total Contribution 2,, less Fixed Cost 93,5 ` 1,6,5 Ans. 3: Item Description ` Revenue per trip 4, Less: Variable Cost Train Fare 1,7 Meals per Child 3 Craft Materials 6 Total Variable Cost 2,6

4 Contribution per child 1,4 Relevant Range = 51813/11 = 513 Step Fixed Cost: Items ` Room Rent (76/4) 19 Transport Cost (12/6) 2 Total Step Fixed Cost 39 Net Contribution = = ` 11. Details Amount Sales Variable Cost 4-26 Contribution 14 At 513 Students General Fixed Cost 518,13 Room Rent 129*76 98,4 Transportation 86*12 13,2 Total Fixed Cost 719,37 Gross Contribution 513*14 718,2 Loss (1,17) BEP = /14 = Hence the Minimum Students will be 514 Relevant Range for Earning Profit will be 514 to 516 Particulars General Fixed Cost 518,13 518,13 Room Rent 98,4 98,4 Transportation 13,2 13,2 Total Fixed Cost 719,37 719,37 Gross Contribution 719,6 722,4 Profit 23 3,3 Ans. 4: Order Qty Order Qty 1-14 (`) (`) Selling Price `/u 3, 3, 1% 3, 3, Sales revenue p. u. 33, 33, Less: Variable purchase cost 29, 26, Contribution / unit (before shipping) 4, 7, Less: Shipping cost > 11 units 5, Contribution/ units after Shipping 2,

5 Order Quantity Upto 14 units Above 14 units ` ` ` ` Selling Price Revenue p.u Less: Variable purchase cost Contribution p.u. (before shipping cost) Less: Shipping Cost p.u. on sales > 11units N.A Cont. p.u. on units > 11units (i) (ii) (iii) (iv) Up to 11 units, Reference will earn a contribution of `4,/u. Between 111 & 14 units, contribution of 4, will be wiped out by 5, on shipping costs. Hence we should not consider range not to be considered since additional fixed costs 2,25, will not be covered by 1 units. Valid consideration, 1 units or 141 to 19 units. Fixed cost of box of 5 cameras is ` 2,25, Logical Ranges (units) Exact 1 units Highest units in their respective ranges No. of Camera Boxes A Cost of Cameras (`) B 4,5, 6,75, 9,, Contribution (`/u) ` 4, C 4, Contribution (`) first 11 7,/u D 7,7, 7,7, Contribution (`) Balance 2,/u E 8, 1,6, Total Contribution (F = C + D + E) (`) F 4,, 8,5, 9,3, Profit (F) (B) (`) G - 5, 1,75, 3, Best strategy buy 15 units from Comp. sell 11 at store and 4 outside. BEP should be between units Extra Camera box cost beyond 15 units = 2,25, Less: Profit for 15 units = 1,75, Extra profit acquired = 5, No. of units to cover this additional costs at contribution 2 `/u = BEP = = 175 units 5, 2, = 25 Alternative way of finding BEP

6 Order Quantity Upto 14 units Above 14 units Cost of Boxes (-) Net Revenue on 1st 11 units (11 4) (11 4) (11 7) (11 7) Net Step Fixed Cost yet to be recovered Cont. p.u. on units > 11units Nil Additional units above 11 units to break even N.A. N.A. N.A. 65 Therefore total units to break even = = 175 units Alternative Solution The problem involves fixed cost of 5 Computers i.e ` 2,25, for incremental sale of 5. Units sold Margin per unit = Sales price buying price + commission ( `) Margin (Excluding shipping cost) 4,4, 5,6, 1,5, 13,3, Shipping cost (`) (3 x 5) (4 x 5) (8 x 5) For sale beyond 11 units = 1,5, = 2,. = 4,, Contribution (`) 4,4, 4,1, 8,5, 9,3, Fixed cost ( Cost of Computers) 6,75, 6,75, 6,75, 9,, Profit -2,75, -2,65, 1,75, 3, Best strategy is sales level at 15 units. The variations of profit is due to incremental fixed cost. From the profits at different levels, it is seen that the BEP lies between 151 and 19. Let BEP = X Units Margin = 7 X Shipping Cost = (X -11)x 5 Cost of Computers = ` 9,, We have, 7 X = (X -11) x Or 7X = 5X Or 2X = 35 or X = 175 Thus, BEP = 175 units. Ans 5: Overhead rate per labour hour = Overhead incurred in first half year = `21,, = `52.5 per labour hour Direct labour hours worked 4, hours Apportionment of technical staff salaries Machine maintenance = 6,37,5 X 31/1 = ` 1,91,25

7 Set up = 6,37,5 X 4/1 = ` 2,55, Quality Inspection = 6,37,5 X 3/1 = ` 1,91,25 Statement showing apportionment of Machine operation and Machine maintenance between stares and production activity (set up) in ratio 2:8 Particulars Machine operation Machine maintenance (`1,87,5 + `1,91,25) Total Expenses 1,12,5 3,78,75 Stores / Receiving 2,2,5 75,75 Set up/ Production run 8,1, 3,3, Particulars Wages and salaries of stores staff Component of set- up cost Total Total Expenses 2,62,5 2,55, Stores / Receiving 2,62,5 - Set up / Production run - 2,55, 19,8,75 5,4,75 13,68, Rate per activity cost driver Particulars Stores / Receiving Total overheads Units of activities carries out Rate per activity cost driver (`) (`) 5,4,75 1, Set up/ Production run 13,68, 2, Quality inspection 1,91,25 1, Statement showing computation of cost of products P and Q (Based on the existing system of single overhead recovery rate) Particulars Product P Q Direct Labour hours Unit made Direct materials cost Direct labour cost Overheads Total cost of products (@ `6 per D.L.H.) `52.5 per D.L.H.) 96 15, 6, 5,76 5,4 62,16 1 5, 4, 6 5,25 9,85 Cost per unit Statement showing computation af cost of products P and Q (Using activity based costing system) Particulars Product P Q

8 Units Direct materials cost Receiving/ Stores cost Receiving Stores cost (48 X ) (52 X ) Production runs / Set ups cost (36 X 67.59) (24 X 67.59) Inspection cost (3 X ) (1 X ) Total Cost products Coat per unit 15, 6, 5,76 13,243 24,141 4,482 5, 4, 6 14,346 16,94 1,494 53,626 36, Computation of sales value per quarter of component K (Using activity based costing system) Units of component K To be delivered per quarter Component of initial design cost per quarter ( `6,/8 quarters) Direct material costs Direct labour cost (6 hours X `6) Receiving cost (5 X `275.89) Production runs cost (6 X `67.59) Inspection cost (24 X `149.41) Total cost Add: Mark up (25% of cost) Sales value Selling price per unit of K (`43,35/3, units) 3, ` 7,5 12, 1,8 5,518 4,24 3,586 34,428 8,67 43, Ans. 6: (a) (i) The target cost of each product after reduction is computed as follows: Product A B C D Present Price (`) Proposed Price (`) (ii) Statement showing cost/unit of Driver as per ABC Target Cost (`) (with 25% Margin) Cost Amount Driver No. Cost/unit of Driver Set-ups 26,25 Production runs 15* `25. Stores receiving 18, Requisition 4** `45.

9 Inspection/Quality 1,5 Production runs 15 `1. Handling/Dispatch 23,1 Orders 21 `11. Machine Department 52,13 Machine Hrs. 6,5 `8.2 * Production runs = (6/2) + (5/2) + (4/2) + (6/2) = 15 ** Requisitions = 1 for each product or 4 total Machine hours = 2,4 + 1, ,8 = 6,5 hours. Statement showing Total Cost and Cost Per Unit as per ABC Item A B C D ` ` ` ` Direct Material 24, 25, 12, 36, Direct Labour 16,8 1,5 5,6 12,6 Set-up 7,5 6,25 5, 7,5 Stores receiving 4,5 4,5 4,5 4,5 Inspection/Quality 3, 2,5 2, 3, Handling/Dispatch 6,6 5,5 4,4 6,6 Machine Dept. Cost 19,248 12,3 6,416 14,436 Total Cost 81,648 66,28 39,916 84,636 Output (Units) Cost per unit (iii) Comparison of Actual Cost and Target Cost Cost A B C D ` ` ` ` Actual Target Difference (-) 3.92 (-) 3.44 (-).21 (+) 1.6 Comment: The total actual cost of A, B and C product is less than the target cost so there is no problem in reducing the cost of these product by `5 from the present price. It will increase the profitability of the company but the cost of D is slightly more than the target cost, it is therefore, suggested that the company should either control it or redesign it. Ans. 7: Costs specific to booking operations: Direct person s salary 2, Mobile expenses 3, Conveyance 4, 27, Share of other overheads: Office space 4, General Telephone 2,4 Security/Maintenance 1,6 Miscellaneous Expenses 1, 9,

10 Total cost allocated to the service 36, Average demand per month = 2, , = 1,2 12 Total Cost per month Total Cost per booking = Average bookings per month = Revenue per ticket = ` 3 Total revenue less total cost = 3-3 = 36, = ` 3 1,2 Assuming that other overheads will anyway exist even of the service is not provided, the manager can hope to achieve a profit of ` 3 1,2-27, is ` 9, for the full year. Minimum average volume to set up the service will be the amount needed to recover the specific costs of this service, is 27, per month. Minimum average books = 27, 3 = 9 bookings Ans. 8: Statement of Equivalent Production in Units Particulars Materials Wages & Overhead % age Units %age Units Units Completed 1% 9 1% 9 Closing W.I.P. 1% 9 5% 9 Equivalent Units Material A Material B Material Variances Standard qty for actual output ** x std price Actual qty X actual price 3 = 59,4 22,275@2.8* = 62,37 4 = 39,6 = 44,649 29,7 99, 33,165 1,7,19 *Actual Cost / Actual Quantity ** Standard Quantity for actual output = ( std qty/ budgeted prod) x actual output MCV = TSC TAC = 99, 1,7,19 = 8,19 (A) MPV = AQ (SP AP) A = 22,275 (3 2.8) = 4,455 (F) B = 1,89 (4 4.1) = 1,89 (A) 3,366 (F) MUV = SP (SQ AQ)

11 A = 3 (19,8 22,275) = 7,425 (A) B = 4 (9,9 1,89) = 3,96 (A) 11,385 (A) MMV = SP (RSQ AQ) A = 3 {19,8 29,7 33,165 22,275} = 495 (A) B = 4 {9,9 29,7 3,165 1,89} = 66 (F) 165 (F) MYV = S. C Per Unit (S. O. For Actual Mix A. O.) = 99, 9,9 {9,9 29,7 33,165 9,9} = 1 ( ,9) = 11,55 (A) Labour Variances: LCV = TSC TAC = 2,4, 12, 9,45 1,91,25 = 2,25 (A) LRV = AH (SR AR) = 48, {4 (1,91,25 48,)} = 75 (F) LITV = No. of Idle hours SR = 48, (47,5 4) = 1,2 (A) LEV = SR (SH AH) = 4 {(6, 12,) 9,45 47,7} = 1,8 (A) (ii) Variable Overhead Variances VOC = Recovered Overheads Actual Overheads = 9, , = 2,25 (F) V.O (Exp.) V = Standard V.O. Actual V.O. = 47,7 1 45, = 2,7 (F) V.O. (Eff.) V = Recovered Overheads Standard Overheads = 9, ,7 = 45 (A) Fixed Overheads Variances FOCV = Recovered Overheads Actual Overheads = (1,2, 12,) 9,45 1,2,9 = 94,5 1,2,9 = 26,4 (A) F.O.(Exp.) V = Budgeted Overheads Actual Overheads = 1,2, 1,2,9 = 9 (A) FOVV = Recovered Overheads Budgeted Overheads = 95,5 1,2, = 25,5 (A) Sales Variances Sales Price Variance = Actual Unit Sold (SP AP)

12 Sales Volume Variance (Contribution Loss) = 9, {5 (4,57,5 9,)} = 7,5 (F) = S. R. of Profit (Budgeted Qty. Actual Qty.) = (6, 12,) (12, 9,) = 15, (A) Ans. 9: Report to the Departmental Manager showing the cost ratios: Standard hours produced 2112 (a) Efficiency Ratio = = 1 = 11% Actual hours worked 192 (b) (c) (d) (e) Standard hours produced 2112 Activity Ratio = = 1 = 82.5% Budgeted Std. Hours 256 Budgeted Std. Hours 256 Standard Capacity usage Ratio = = 1 = 8% Maximum Possible Hours 32 Actual hours worked 192 Actual Capacity utilisation Ratio = = 1 = 75% Budgeted hours Calendar Ratio = 1 96% 25 = (ii) Report to the Departmental Manager Setting out the analysis of variances Standard fixed overhead rate per hour = 1536 = Rs A. Fixed Overheads Rs. (a) Charged to production (2112 6) (b) Actual hours Std. rate (192 6) 1152 (c) Revised budgeted hours Std. rate ( ) (d) Original budgeted overheads 1536 (e) Actual overheads 165 Variances: Efficiency variance (a-b) Capacity variance (b-c) Calendar variance (c-d) Volume variance (a-d) Expenditure variance (d-e) Total variance 1152(F) 3226(A) 614(A) 2688(A) 114(A) 3828(A) B. Variable overheads:

13 Standard variable overhead rate per hour = =Rs.8 (a) Charged to production (2112 8) (b) Actual hours Std. rate (192 8) 1536 (c) Actual overheads 145 Variances: Efficiency variance (a-b) Expenditure variance (b-c) Total variance (a-c) 1536(F) 86(F) 2396(F) Working note: Maximum possible hours ( ) 32 Budgeted hours: 32 less 2% downtime 256 Actual hours 192 Budgeted standard hours 256 Standard hours produced 5112 Budgeted working days 25 Actual working days 24 Ans. 1: Details of original and revised standards and actual achieved Original standards Revised standards Actual Fruit 4 Kgs Rs16 Rs6,4 4 Kgs Rs 19 Rs7,6 428 Kgs Rs 18 Rs7,74 Glucose 7 Kgs Rs1 Rs7, 7 Kgs Rs12 Rs 8,4 742 Kgs Rs 12 Rs 8,94 Pectin 99 Kgs Rs 33.2 Rs Kgs Rs 33.2 Rs Kgs Rs 32.8 Rs 4,1 Citric acid 1 Kg Rs 2 Rs 2 1 Kg Rs 2 Rs 2 1 Kg Rs 95 Rs 95 1,2 kgs Rs16, ,2 kgs Rs19, ,296 kgs Rs2,83 Labour Rs 585. Rs 585. Rs 6 1,2 kgs 17, ,2 kgs 2,71.8 1,296 kgs 21,43 Loss 36 kgs 36kgs 132 (i) Planning variances 1,164kgs Rs 17, ,164kgs Rs 2,71.8 1,164 Kgs Rs 21,43 * Fruit extract (6,4 less 7,6) Rs 1,2(Adverse) Glucose syrup (7, less 8,4) Total * (Std qty Std price less Std qty Revised Std price) (ii) Ingredients operating variances Rs1,4(Adverse) Rs 2,6(Adverse)

14 Total (19,486.8 less 2,83) = Rs 1,316.2(Adverse) Ingredients Price variance (Revised Material Price Actual Material Price) ( Actual Qty Consumed) Variance in Rs Fruit extract (19 18) (F) Glucose syrup Nil Pectin ( ) 125 5(F) Citric acid (2 95) 1 15(F) 583(F) Usage variance (Std Qty on Actual Production less Actual Qty on Actual Production) Revised Std Price/Unit Rs Variance in Rs Fruit extract (4 428) (A) Glucose syrup (7 742) 12 54(A) Pectin (99 125) (A) Citric acid Nil 1,899.2(A) (iii) Mix Variance (Actual usage in std mix less Actual usage in actual mix ) std price Variance in Rs Fruit extract ( ) 19 76(F) Glucose syrup ( ) (F) Pectin ( ) (A) Citric acid (1.8 1) 2 16(F) 34.3 (A) Yield variance (Actual yield Std yield from actual output) Std cost per unit of output = (1,164 1,296.97) = 1,558.9(A) Labour operating variance = 15(A) (iv) Total variance = Planning variance + Usage Variance + Price Variance + labour operating Variance. Or Total Variance = (2,6) + ( 1,899.2 ) (15) = (A). Ans. 11: (i) Under Traditional Standard Costing System: Fixed overhead volume variance = Absorbed Fixed Overhead Budgeted Fixed Overhead

15 = Actual Output Std. Fixed Overhead p.u. - Budgeted Fixed Overhead = 88 units 2 2 = `24 (A) 1 Total Fixed overhead variance = Absorbed Fixed Overhead Actual Fixed Overhead = Actual Output Std. Fixed Overhead p.u. - Actual Fixed Overhead = 88 units = Nil 1 (ii) Under Activity Based Costing System: Total Fixed Overhead Variance = Absorbed Fixed Overhead Actual Fixed Overhead = Std. Batches for actual output Std. Fixed Overhead rate p. batch Actual Fixed Overhead = 9 batches 2 1 units 1 units p.batch = `4 (F) *Std. Batches for actual output = 88 units 1 units 1 units p.batch 1 units = 8.8 batches or 9 batches (since batches can t be in fraction) Ans. 12: Solution SR SH SR RSH SR AH AR AH Skill Semi-Skill Unskilled Workings Note: Standard hours produced = 27 Standard Mix: 27 9 = 3 Sub-efficiency Variance Gang Variance Rate Variance 35 (A) 12 (F) 4 (A) Cost Variance = 27 (A) Skill Semi-Skill Unskilled Ratio 4: 3: 2: Hrs Actual hrs = 4 9 = 36 hrs. Actual hrs in Standard Ratio = 36 4: 3: 2:

16 = 16 = 12 = 8 [(Standard Rate = Actual Rate) Actual hrs.]= Rate Variance Semi-skilled = 16 (3 2) Actual hrs = 16 Actual hrs = 16 (for semi-skilled) Actual Semi-skilled = 2 (Unskilled actual) 16 = 2 (Unskilled) Unskilled hrs (actual) = (16 2) =8 Total Actual = 36 Actual hrs skilled = 36 (16 + 8) = = 12 Actual Hrs. Skilled Semi-skilled Unskilled hr week = 3 = 4 = No. of Workers (i) (ii) (iii) (iv) (v) Gang Variance: = (Actual Hrs in Standard Ratio Actual Hrs in Actual Ratio) Standard Rate = = 12 (F) Sub-efficiency Variance: = Standard Rate (Standard Hrs Actual Hrs in Standard Ratio) = = 35 (A) Total Labour Rate Variance: = Actual Hrs (Standard Rate Actual Rate) = = 4 (A) Labour Cost Variance: = (Standard Rate Standard Hrs Actual Rate Actual Hrs.) = = 27 (A) Ans. 13: Working Notes 1. Material data Standard data for actual output Actual output 6,4 units Actual data for actual output Quantity Kgs. Price Per Kg. Amount Rs. Quantity Kgs. Price Per Kg. Amount Rs. 32, 8 2,56, 36, 7.5 2,7, 2. Labour data

17 Standard data for actual output Actual output 6,4 units Actual data for actual output Labour hours Rate/hour Rs. Amount Rs. Labour hours Rate/hour Rs. Amount Rs. 32, 8 2,56, 36, 7.5 2,7, 3. Variable overheads data Standard/Budgeted data Budgeted variable overheads for actual hours Standard variable overhead Rate/hour Standard variable overhead rate/ unit Actual data 6,5, Actual variable overheads 6,48, (Rs.) Actual Units 6,4 Actual Hours 65, Rs. 1 Rs Sales data Sales Units 6, Budgeted data Budgeted Margin p.u. Rs. 5 (Rs. 25 Rs. 2) Amount Rs. Sales Units 3,, 6,4 Actual data Actual Margin p.u. Rs. 65 (Rs. 265 Rs. 2) Amount Rs. 4,16, 1. Market Size Variance = Budgeted market share percentage [Actual industry sales in units Budgeted industry sales in units] Budgeted contribution margin per unit =.12 [6, units 6, units/12%] Rs. 5 =.12 [6, units 5, units] Rs. 5 = Rs. 6, (F) 2. Market Share Variance = [ =[ ] 6, units X 5 = (6,4 units 7,2 units) Rs. 5 = Rs. 4, (A) 3. Gross Margin Sales Volume Variance = (Actual quantity Budgeted quantity) Budgeted margin per unit = (6,4 units 6, units) Rs. 5 = Rs. 2, (F) 4. Gross Margin Sales Price Variance = (Actual margin per unit Budgeted margin per unit) Actual quantity of units sold = [(Rs. 65 Rs. 5) 6,4] 6,4 units = Rs. 96, (F) 5. Direct Material Usage Variance = (Standard quantity Actual Quantity) Standard Price per kg. = (32, kgs 36, kgs.) Rs. 8 = Rs. 32, (A) Direct Material Price Variance = (Standard price/kg. Actual price/kg.) Actual quantity of material used = (Rs. 8 Rs. 7.5) 3,6 kgs. = Rs. 18, (F)

18 6. Direct Labour Efficiency Variance = (Standard labour hours Actual labour hours) Standard rate per hour = (64, hours 65, hours) Rs. 6 = Rs. 6, (A) Direct Labour Rate Variance = (Standard labour rate per hour Actual labour rate per hour) Actual time taken in hours = (Rs. 6 Rs. 6.4) 65, hours = Rs. 26, (A) 7. Variable Overhead Efficiency Variance = (Standard hours for actual output Actual Hours) Standard variable overhead per hour = (64, hours 65, hours) Rs. 1 = Rs. 1, (A) Variable Overhead Expense Variance = Budgeted Variable Overhead Actual Variable Overhead = Rs. 6,5, Rs. 6,48, = Rs. 2, (F) Operating Statement (Reconciling the budgeted contribution with actual contribution Rs. Rs. Rs. Budgeted Contribution 3,, Gross margin sales volume variance 2, - Gross margin sales price variance 96, - 1,16, 4,16, Cost Variances Material usage - 32, Material price 18, - Labour efficiency - 6, Labour rate - 26, Variable overhead efficiency - 1, Variable overhead expense 2, - 2, 74, 54, Total Actual Contribution 3,62, Verification: Actual Contribution = Actual sales revenue Actual variable costs = Rs. 16,96, [ RS. 2,7, (actual material cost) + Rs. 4,16, (actual labour cost) + Rs. 6,48, (actual variable overheads)] = Rs. 16,96, Rs. 13,34, = Rs. 3,62, Ans. 14: (i) Reconciliation Statement showing which factor has contributed to change in profit Increase in contribution due to increase in volume (` 28 lakhs `24 lakhs) (Refer to working note 3) Favourable in ` (lakhs) 4 Sales price variance 14 (Refer to working note 3) Material usage variance 52 (Refer to working note) Adverse in ` (lakhs)

19 (ii) Material price variance (Refer to working note 4) Direct Labour rate variance (Refer to working note 4) Direct labour efficiency variance (Refer to working note 4) Fixed overhead expenditure variance (Refer to Working note 3) Total change in profit Break-even sales (year 1) (Refer to working note 3) = Break even sales (year 2) (Refer to working note 3) = Fixed costs P/V ratio Rs.16 lakhs = =`8 lakhs Rs.24 lakhs Rs.1,2 lakhs Rs.13 lakhs =`962.5 Rs.48 lakhs Rs.1,54 lakhs (iii) Percentage increase in selling price needed over the sale value of year 2 to earn a margin of safety of 45% in year 2. P/V ratio = (`48 lakh / `1,54 lakhs 1 = % Break even sales = Rs lakhs % Rs.1,54 = (5,83,333 5,4,) `12 `52 lakhs (Fav.) If Margin of safety to be earned is 45% then Break-even point should be 55%. Contribution increase required = Revised contribution = 1,54 lakhs % Present contribution Increase in selling price required Percentage increase in selling price Over the sales value of year 2 = Working notes: 1. Budgeted sales in year 2 = ` lakhs = `48 lakhs = %55 55 = `65.45 lakhs (` lakhs `48 lakhs) Rs lakhs 1 = 4.25% Rs.1,54 Lakhs If actual sales in year 2 is `11 then budgeted sales is `1

20 Rs.1 If actual sales in year 2 is Re1 then budged sales = Rs.11 If actual sales in year 2 is `15,4,, then budged sales are = Rs.1 `15,4,, Rs.11 = `1,4 lakhs 2. Budged figures of direct material; direct wages; and variable overhead worked out on the basis of % of sales in year 2: Direct material % to sale (in year 1) = Direct material cost 1 Sales 6 = 1 = 5% 1,2 Budgeted figure of direct Material (in year 2) = 5% `1,4 lakhs = `7 lakhs Direct wages and variable overhead % to sales (in year 1) = Direct wages and variable Sales overhead 1 3 = 1 = 3% 1,2 Budgeted figure of direct wages and variable overhead (in year 2) = 3% 1,4 lakhs = 42 lakhs 3. Statement of figures extracted from working results of a company. (Figures in lakhs of `) Year 1 Actual Years 2 (Budgeted) Years 2 Actual Total variance (a) (b) (c) (d)=(c)-(b) Sales (A) 1,2 1,4 1,54 14 (Fav) (Refer to w.n. 1) Variable costs: Direct material (Fav) (Refer to w. n. 2) Direct wages and variable (Fav.) overhead (Refer to w. n. 2) Total variable costs (B) (Fav.) Contribution (C) = [(A) (B)] (Fav)

21 Less: Fixed cost (Adv.) Profit (Fav.) 4. (i) Data for Material variances: (ii) Quantity of material m/t Standard data for actual output Rate per m/t Amount Quantity of material m/t Actual data Rate per m/t Amount ` ` ` ` 5,83, lakhs 5,4, lakhs Material price variance = (Standard rate Actual rate) Actual quantity = Nil Material usage variance = (Standard quantity Actual quantity) Standard rate per m/t = (5,83,333 5,4,) `12 `52 lakhs (Fav.) Date for Labour and variable overhead variances Labour hours Standard data for actual output Rate per hours Actual data Amount Labour hours Rate per hours Amount ` ` ` ` 87,5, lakhs 8,, lakhs Labour rate variance: = (Standard rate Actual rate) Actual labour hours = (`4.8 `5.15) 8,, = `28 lakhs (Adv.) Labour and variable overhead efficiency variance: = (Standard labour hours Actual labour hours) Standard rate per hour = (87,5, 8,,) `4,8 = `36 lakhs (Adv.) Ans. 15: Statement of Ranking Working Notes Products Particulars A B C Selling Price/unit (Rs.) Variable cost/unit (Rs.) Direct material Direct labour Variable overheads Contribution/unit Units

22 Total contribution Ranking III II I Raw material per unit (kg) Contribution per kg (Rs.) Ranking III II I DLH required per unit Contribution per DLH Rs. 45 Rs. 4 Rs. 55 Ranking II III I Solution (a) Raw material available will be only 121 kg Product Ranking No. of units RM (kgs) CPU Total contribution C I B II A III 55 (33/.6) 33 (B.F.) Total 121 Rs Less: Fixed overheads 138 Profit 1175 (b) Direct labour hours available will be only 5 hours Product Ranking No. of units DLH CPU Total contribution C I A II B III 5 (1/.2) 1 (B.F.) 8 4 Total 55 Rs. 24 Less: Fixed overheads 138 Profit 12 (c) No shortage of materials and labour: Ranking as per total contribution is to be considered. Product Ranking No. of units CPU Total contribution C I 25 (2 + 25%) B II A III Total Rs Less: Advertisement cost 2 Net contribution 335 Less: Fixed overheads 138 Profit 1655 Ans. 16: Bloom Ltd. Peak Season. Statement of Contribution and BEP (in units) Figures Rs. Product A B C A. Selling Price per unit

23 Variable Costs per unit: Direct Material Direct Labour Variable Overhead Production Variable Overhead-Selling B. Total Variable Cost C. Contribution / unit (A B) D. Direct Labour hours / required per unit E. Contribution per Labour Hour (C / D) F. Ranking General Fixed Overhead 2, Specific Fixed overhead 2, 4,78 6,78 G. Total Fixed Overhead 26,78 H. BEP (units) (for only 1 Product at a time) (G/C) 2, 1 22, 24, = 2 = 2 = 236 Maximum units that can be produced of product C with limited labour hours 1,617. 1,617 = = < Break Even units. Hence, Bloom Ltd. cannot produce C. Next rank = A Maximum units of A that can be produced with limited labour hours = Break Even units of A = 2 Profit if only A is produced Rs. Contribution = Rs ,2 Fixed Cost 2, Profit 2 Off Season 1,617 = 22 units. 8 Bloom Ltd. Off Season Statement of Contribution and demand Figures Rs. per unit Product A B C A Selling Price Direct Material Direct Labour Production-Variable Overhead B Total Variable Cost

24 C Contribution per unit (A B) Ranking Maximum demand Overall limit of production 215 units Statement of profitability under different options (Limit of production = 215 units) A B C Total Fixed Profit Cost (Loss) Contribution per unit Option 1: Units Contribution (Rs.) - 14,375 12,1 26,475 26,78 (35) Option 2: Units Contribution (Rs.) 12, 14,375-26,375 22, 4,375 Option 3: Units Contribution (Rs.) 9,6-16,335 25,935 24,78 1,155 Best strategy is to produce 1 units of product A and 115 units of product B during offseason. Maximum profit = Rs. 4,375. (i) Best strategy for peak-season is to produce 22 units of A. (ii) Maximum profit for off-season Rs. 4,375. Ans. 17: Working Notes 1. Computation of total labour hours available Departments No of workmen days Hrs/day Total hours (a) (b) (c) (d) (e) = (b) x (c) x (d) A , B ,4 C ,2 D , Computation of hours required per unit of each product Departments Product P Product Q Wages Wage/hr HRs Wages Wage/hr Hrs.

25 (Rs.) (Rs.) (Rs.) (Rs.) (a) (b) c=(a)/(b) (d) (e) (f) = (d)/(e) A B C D Total hours per unit: Statement showing maximum output permissible Departments Hours Product P Product Q Available Hrs. required/ Maximum Hrs. required/ Maximum Unit output in unit output in Units Units (a) (b) (c)=(a)/(b) (d) (e)=(a)/(d) A 72, 6 12, 9 8, B 38,4 3 12,8 6 6,4 C 43,2 9 4,8* D 57, ,8* Total hours p.u.: This shows that either 4,8 units of product P or Q can be obtained by utilising the available hours in the four departments. 4. Product wise contribution per hour Product P Rs. Product Q Rs.

26 Selling price p.u. (A) Total raw material cost p.u. (Rs Rs. 8) (Rs Rs.32) 3 6 Total wages per unit (Rs Rs.18 + Rs. 54) (Rs Rs Rs. 72) Variable overheads p.u Total variable cost p.u. (B) _161 _236.3 Contribution p.u. [(A) (B)] Labour hours p.u Contribution per labour hour (Rs. 54/18hours)(Rs. 83.7/27 hours) (a) Though the contribution per labour hour of product Q is better but there is a constraint viz, the numbers of workers in each department can neither be interchanged nor newly recruited, hence due to this following two alternat8ives would arise which may help in deciding about the product mix to yield maximum profit. Alternative I: Producing 4,8 units of product Q and utilising the remaining available hours of labour or making units of product P. Alternative II: Product 4,8 units of product P and utilising the remaining available hours of labour for making units of product Q. Statement of Product mix under alternative I Departments Available Hrs. required Remaining Hrs./ units of Units Hours for 4,8 units of Q hours Product P of product P (a) (b) (c)=(a)-(b) (d) (e)=(c)/(d) A 72, 43,2 28,8 6 4,8 B 38,4 28,8 9, C 43, ,2 9 4,8

27 D 57,6 57,6 Nil The above table shows that out of the available hours under alternative I; 4,8 units of product Q and 3,2 units of Product P can be made. Statement of Product mix under alternative II Departments Available Hrs. required Remaining Hrs./ units of Units Hours for 4,8 units of P hours Product P of product Q A 72, 28,8 43,2 9 4,8 B 38,4 14,4 24, 6 4, C 43,2 43, D 57, ,6 12 4,8 The above table shows that out of the available hours under alternative II; 4,8 units of Product P and 4, units of product Q can be made. Profit Statement under above alternatives Products First alternatives Second alternatives Units Contribution Amt. Units Contribution Amt. P.u. (Rs.) Rs. p.u. (Rs.) Rs. P 3, ,72,8 4, ,59,2 Q 4,8 83,7 4,1,76 4, ,34,8 Total Contribution: 5,74,56 5,94, Less: Fixed cost p.a. 1,44, 1,44, Profit 4,3,56 4,5, Second alternatives is the most profitable product mix. Alternative Solution By LPP

28 Formulation: Maximize, Z (Contribution) = 54x y s.t.c., 6x + 9y 72 [Department A s capacity] 3x + 6y 384 [Department B s capacity] 9x 432 [Department C s capacity] 12y 576 [Department D s capacity] For the line, 6x + 9y = 72 For the line, 3x + 6y = 384 x 12 y 8 x 128 y 64 6x + 9y = 72 3x + 6y = 384 9x = y = A(,48) B(32, 48) 4 C(48, 4) E(,) D(48,)

29 ABCDE is feasible region Points Coordinates Value of Objective Function A, B 32, C 48, D 48, 2592 E, Z max = 594 when x is 48 and y is 4 Profit at this production mix = ` = ` 45 (b) Statement of most profitable product if only one product is to be manufactured Products P Q Contribution per unit (Rs.) : (A) Maximum possible output (in units): (B) 4,8 4,8 Total Contribution : (A) x (B) 2,59,2 4,1,76 Product Q is to be preferred. Statement of most profitable product if only One product is to be manufactured And licence to import the raw material is only For materials worth Rs. 1,8, Product P Q Raw material required p.u. (Rs.) 3 6 Permissible output in units out of imported material of

30 Rs. 1,8, 6, 3, Maximum output possible in the available hours 4,8 4,8 Output possible keeping in view the availability Of imported material and Labours hours (units) 4,8 3, Contribution per unit (Rs.) Total Contribution (Rs.) 2,59,2 2,51,1 (4,8 units x Rs. 54) (3 units x Rs. 83.7) Product P is to be preferred (i.e. answer differs) because of import licence restriction, which is only available for purchasing material worth only Rs. 1,8,. Ans. 18 W. Note 1 W. Note-2: Rs. p. u Rs. p. u. A B Material 2 4 Variable production overhead cost 28 4 TVC 3 44 Selling price 6 7 (a) Contribution 3 26 (b) Limiting factor (hr./u) (c) Contribution/hr. (a/b) Rs (d) Rank II II (e) Budgeted production & sales 1,2, 45, (f) Maximum demand 1,44, 54, Total Fixed cost Rs 14,7, Fixed overhead recovery rate =(Amount Budgeted hours) = 14,7, 36,75 = Rs. 4/hr. Budgeted hours A 1,2, Rs..25 = 3, hrs. B 45, Rs..15 = 6,75 hrs. 36,75 hrs. (a) A B Contribution per unit Rs Less: Fixed overhead per unit Rs. 1 6

31 (a) Profit per unit Rs. 2 2 (b) Units 1,2, 45, Total (a b) 24 lakhs + 9 lakhs = 33 lakhs Management is indifferent on the basis of profit per unit however this is wrong concept on selecting the product mix. (c) (b) A B (a) Contribution per unit Rs (b) Limiting time/unit.2.15 Contribution /hr. (a/b) Rs. 1,5 Rs. 1,733 Rank II II Available 3,75 Statement of product mix & profit Hrs. units Contribution/u Total Less: for Rank I 81 54, 26 14,4, For Rank II 2,265/.2 1,13, ,97,5 Product A 48,1,5 Less: Fixed cost 14,7, Profit 33,31,5 Return per bottleneck hour = (selling price material cost)/ (Time on bottleneck resource) Product A Product B = Rs. 2,9 [(Rs. 6 Rs. 2)/ Rs..2 hours] = Rs. 2, [(Rs. 7 Rs. 4)/.15 hours] Product A should be sold up to its maximum capacity of utilizing 2,88 bottleneck hours (1,44, units.2 hours). This will leave 195 hours for product B thus enabling 13, units (195/.15) to be produced. The maximum profit is calculated as follows: Note: Throughput return from product A (1,44, Rs. 58) 83,52, Contribution from product B (13, Rs. 3) 3,9, 87,42, Less: Variable overheads 35,4, Fixed overhead cost 14,7, Net profit 37,32, It is assumed that the variable overheads (e.g. direct labour) are fixed in the short term. They are derived from part (a) [(12, Rs. 28) + (45, Rs. 4)] Ans. 19: Particulars X Y Z 1. Sale Price p.u. Rs.66 Rs.75 Rs.9 2. Material and Other Variable Cost p.u. Rs.24 Rs.3 Rs.4 3. Contribution p.u. (1 2) Rs.42 Rs.45 Rs.5 4. Bottleneck Resource Time (min) Rs.

32 5. Product Return per minute [(3) (4)] Rank based on (5) above II I III 7. Factory Cost per minute = Rs.2,21,6 75, Throughput Accounting (TA) Ratio = (5) (7) Rank based on TA Ratio II I III Comments: Product Y has the highest throughput Contribution per minute and the highest TA Ratio Ans. 2: Working Notes: (i) Variable Cost per unit of products A, B & C Products A B C Cost of parts Frame E F G Wages of skilled labour Wages of unskilled labour Variable Overheads (ii) Sales quantity of products A, B & C: Products A B C Sale Price (per unit) Less: Variable Cost (per unit) Contribution per unit The current ratio of sales in quantity of A, B & C is 1:2:4 Suppose number of units sold of A=x, B = 2x & C = 4x Fixed overhead per month = Rs Rs Rs. 845 = Rs. 3 Total profit per month = Rs = 1 1x + 15 (2x) + 3 (4x) = Rs. 3 + Rs. 1 Or x = Rs. 25 units Sales quantity of products are A = 25 units; B = 5 units & C = 1 units (a) Sales Budget in quantity as well as in value for A, B & C Products A B C Sales (units) Selling price per unit Rs. 45 Rs. 55 Rs. 65 Sales value Rs Rs. 275 Rs. 65 (b) Production Budget A B C Sales (in units)

33 Add: Closing Stock (units)-9% of opening stock Less: Opening Stock Production Budget (units) (c) Parts Usage Budget Parts of material required Products Units to be products Frame E F G A B C (d) Purchase Budget (in quantity as well as in value) Name of parts Frame E F G Parts usage (in units) Add: Closing Stock Less: Opening Stock Quantity (in units) Price per part (Rs.) Purchase value (Rs.) (e) Manpower budget Products Units to be produced Labour Hours Per part Total Skilled Unskilled Skilled Unskilled A B C Wages per hour (Rs.) 6 5 Rs. 384 Rs. 536 Ans. 21: Transfer Price is Rs. 4,5 for each consulting day. Profit mark-up = 15% Let cost = x 15 Profit = x = 1.5x 1

34 Cost + profit = Transfer price x + 1.5x = 4,5 2.5x = 4,5 x = 1,8 Cost = Rs. 1,8 and profit = 1.5x = 1.5 1,8 = Rs. 2,7 Variable cost (8%) = Rs. 1,8 8% = Rs. 1,44 Fixed cost (2%) = Rs. 1,8 2% = Rs. 36. Scenario (i): Every consultancy team is fully engaged. There is no idle time or spare capacity. Hence, transfer price = Marginal cost plus opportunity cost Marginal cost = Rs. 1,44 Saving for internal work = Rs. 2 Net Marginal Cost = Rs. 1,24 Opportunity cost is the lost contribution. Lost contribution = Contribution from external client = Fee charged from external client Variable cost = Rs. (4,5 1,44) = Rs. 3,6. Transfer price = Rs. 1,24 + 3,6 = Rs. 4,3 per consulting day per team. Scenario (ii): One team is idle. Idle time has no opportunity cost. Variable cost for internal work is Rs. 1,24 per consulting day. Second team is busy. Hence opportunity cost is relevant in case of second team. Hence charge of second team is Rs. 4,3 per consulting day per team. Average of charge of two teams = Rs. (1,24 + 4,3) / 2 = Rs. 2,77 per consulting day per team. Scenario (iii): New client offers a fee of Rs. 15,84, Duration: 5 days of 48 weeks 2 teams = 48 days Fee per day 15,84, / 48 = Rs. 3,3 Variable cost = Rs. 1,44 Contribution Rs. (3,3 1,44) = Rs. 1,86 Fee for consulting day for internal work: Variable cost = Rs. 1,24 Contribution lost = Rs. 1,86 Fee to be charged = Rs. 3,1 per consulting day per team. Ans.22: The transfer price will be notional revenue to S and notional cost to T. (a) S will continue to produce more output until the costs of further production exceed the transfer price revenue. (b) T will continue to want to receive more output from S until its net revenue from further processing is not sufficient to cover the incremental transfer price costs.

35 Output Units Division S Incremental Cost Rs Division T Incremental Costs Rs Since S will continue to produce more output if the transfer price exceeds the incremental costs of production, a price of at least Rs.2 per 1 units (Rs. 2 per unit ) is required to persuade the manager of S of produce as many as 1, units, but a price in excess of Rs.25 per 1 units would motivate the manager of S to produce 1,1 units (or more). By a similar argument, T will continue to want more output from S if the incremental revenue exceed the transfer costs from S. If T wants 1, units the transfer price must be less than Rs.22 per 1 units. How ever, if the transfer price is lower than Rs.2 per 1 units, T will ask for 11 units from S in order to improve its divisional profit further. In summary (a) The total company profit I maximised at 1, units of output. (b) Division S will, want to produce 1, units, no more and no less, if the transfer price is between Rs.2 and Rs.2.5(Rs.2 to Rs.25 per 1 units). (c) Division T will want to receive and process 1, units, no more and no less, if the transfer price is between Rs.2 and Rs.2.2 (d) A transfer price must therefore be selected in the range Rs.2. to Rs.2.2 per unit(exclusive). Thus, if a price of Rs.2.1 per unit is selected, profits at 1, units of output would be; (Rs.) Particulars Division S Division T Total Sales/Net revenue Costs Profit 2,1 1,2 9 4, 2,1 1,9 4, 1,2 2,8 At a transfer price of Rs.2.1 any increase in output above 1, units, or shortfall in output below this amount, would reduce the profits of company as a whole, but also the divisional profits of S and T. Ans. 23: (i) Y will pay only a maximum of Rs. (64-64) = Rs. 576 so that its outside purchase cost is matched. i.e Maximum Transfer price by Y = 576 Rs. per unit. Gears Engines (no. of units) Market demand is limited to 2, 2, Market demand is limited to 15, 1, Market demand is limited to 18, 24, Gears Engines Total Hours per unit 4 1

36 Hours available 96, Units possible 24, or 96, (ii) (a) Outside Demand 2, 2, Hours required 8, 2, Units required by Y 5, Hours required 2, Contribution per hour 36 3 Maximise Sales so that hours= 8, 16, Hours used for Y 4, 16, Contribution per units of Y required 1, 4, On units transferred to Y 3 x 16, + 36 x 4 = 48, + 1,44, = 6,24, Contribution per units = 6,24,/5, = Minimum Transfer price per unit = Contribution + variable cost = = Rs (b) Gears Eng. Market Demand 15, 1, Hours required per unit 4 1 Hours required 6, 1, Spare capacity available = 26, Units of Gears possible = 26, per unit = 6,5 Required For transfer = 5, Since spare capacity is used, minimum transfer Price = variable cost of manufacturing = = 496 (c) X will agree to anything above Rs. 496 per unit Market Demand Units 18, 24, Hours per units 4 1 Hours required 72, 24, Hours required for Y s demand 2, This will be need by sacrificing production of Engines. Hence contribution per hours for transferred Units must be atleast.

37 Contribution Required on 5 units = 2, x 3 = 6,, Contribution Required per unit = 6,, = 12 Rs. 5, Minimum Transfer Price = Contribution per unit + Variable Cost = = Rs. 616 per unit Gears and Engines earn a contribution. Variable Cost of in house manufacturing of imported Components = = 56 Production Outside = Rs. 64 Rs. 8/- per unit is being paid for outside purchase Contribution Lost per unit of facility X = 8/4 = 2 hrs. Since X is earning higher contribution per hours 36 & 3 for each product, the management will not have to interfere in situation (a) & (c) where full production capacity is used for outside sales. In (i) (b) Management need not interfere since it is a win-win situation. Departments can negotiate in the relevant range between 496 and 576. Ans. 24: (a) Div A B B Rs. / unit Rs. / unit Rs. / unit Direct Material (Other than A) 5 24 Direct Labour Variable Overhead (Production) 2 2 Variable Production Cost (excl. A) From A 144 From Outside 16 Variable production Cost / unit Selling Price From outside 16 3 Less: Selling Overhead Net Selling Price (outside) Net Selling Price to B 144 Net Selling Price to S 25 Net Selling Price (outside) Variable Production Cost Contribution / unit (outside) (Sale to B & S respectively) Variable Production Cost

38 Contribution / unit Best strategy A = Maximise Production; Sell maximum no. of 18, 52 = 9,36, 52 / unit (outside) (To B) remaining units 2, 49 = 98, Total Contribution for A 1,34, Best strategy for B: Maximise contribution / unit by selling outside and procuring from A 9 / unit Contribution 2, units Balance units can yield contribution of either 74/ unit for outside or Rs. 5 / unit to S Ltd. Production Capacity = 28,. Option I Option II Outside Sales Sales to S Outside Sales contribution / unit 2, 74 = 14,8, 6, 5 = 3,, 24, 74 = 17,76, 2, 9 = 1,8, 2, 9 = 1,8, 16,6, 3,, Total Contribution (16,6, + 3,,)19,6, 19,56, (B) Choose Option I i.e. get 2, units from A, sell 6, units to S and 2, to outside. Make 28, full capacity. Total Contribution Rs19,6,. If A and B are allowed to act independent of the group synergy, Rs. Total contribution A 1,34, B 19,6, Total contribution for X Ltd. 29,94, Cost from X Ltd. s Perspective Variable Cost of production Div A Rs. 95 Div B Variable cost of production other than A 4 4 A supplied by Division 95 A Variable Cost A purchased Option I Outside 26, units Option II Outside 2, ( ) 27,8, 2, ( ) 27,8, 2, (274 2) 1,48, 6, (274 2) 4,44, 22, S Ltd. 6, units (25 2) 3,, 32,28, 32,24,

39 Choose Option I Contribution = Rs. 32,28, for X Ltd. as a whole Transfer (2, units) Make A transfer all output to B. Sell 6, units of B to S and 22, units to out side market. This will make X Ltd. better off by 32,28, 29,94, = Rs 2,34, (i.e. 18, units of A sold to outside increases contribution to A by 3 Rs. / unit and decreases contribution to B by 16 Rs. / unit Net negative effect = 13 18, = Rs.2,34,). Ans. 25: Capacity of X division = 7 units X has the following option to sell following number of units: Option Domestic Market Export Transfer Hiring out (equivalent unit) I II 5 8 l2 III 5 2 IV According to the condition given in (iii) for procurement policy of Y, For 7 units, maximum amount Y is agreeable to pay at market rate i.e Rs 9 per unit = 7 x Rs 9 = Rs 63,, If X transfers l2 units to Y, It has to incur expenses for 58 units from market = = 58 x Rs 92 = Rs 53,36, It means for l2 units from X, Y will pay = Rs ( 63,, 53,36, ) = Rs 9,64, = Rs per unit If X transfers 2 units to Y and Y buys 5 units,, Y can pay to X only = Rs ( 63,, 5 X 92) = Rs l7,, = Rs 85. per unit If transfer of less than l units to Y, X can claim transfer price of Rs 9 per unit Realization ( Rs) Option I 6 x l + 8 x x 9 Rs 69,, Option II 5 x ll2 + 8 x 9 + l2 X Rs 72,84, Option III 5 x ll2 + 2 x 85 Rs 73,, Option IV 5 x ll2+ 8 x x 9 plus contribution from hiring out Rs 66,8, plus Above table shows that Option III is preferable in comparison to Option I and II. If Option III for X, transfer price will br Rs 85. per unit. For taking a decision on option IV, contribution from equivalent unit from hiring out has to be compared with contribution from minimum sales realization of Rs 775 because sales realization of Rs 775 per unit from equivalent 8 units gives the amount of Rs 6,2, which makes up the gap between option III and option IV. In that case, transfer price will be Rs 9 per unit.

40 Ans. 26: Alternative 1 (Conversion versus immediate sale) Sales revenue 9 units at `3 per unit (Refer to working note 1) Less: Relevant costs Material XY opportunity cost (Refer to working note 2) Material A `9 per unit (Refer to working note 3 Material B 1, `45 per unit (Refer to working note 4) Direct Labour : Unskilled 5, `3 per hour 15, Semi-skilled Highly skilled 5, `11 (Refer to working note 5) Variable overheads 15, Re.1 (Refer to working note 6) Extra selling and delivery expenses 27, Nil ` ` ` 21, 54, 45, 55, 7, 15, 2,7, Extra advertising 18, 45, 2,5, Fixed advertising (To remain same, not relevant). Excess of relevant revenues 2, Alternative 2 (Adaptation versus Immediate Sale) Saving on purchase of sub-assembly Normal spending 1,2 `9 per unit 1,8, Less: Revised spending 9 `1,5 per unit (Refer to working note 7) Less: Relevant costs: Material XY opportunity cost (Refer to working note 2) Material C 1, `37 (Refer to working note 8) Direct labour Unskilled 4, `3 per hour 12, Semi-skilled Nil Nil 9,45, 1,35, 21, 37,

41 Highly skilled 4, per hour (Refer to working note 5, 6) Variable Overheads 9, Re.1/- per hour (Refer to working note 6) 44, 56, 9, 1,23, Fixed overheads Nil. Net relevant savings 12, Evaluation : The evaluation of two alternatives clearly shows that Alternative 1, yields higher net revenue of `8, (`2, `12,). Hence because of higher net revenue of Alternative 1, it is advisable to convert material XY into a specialized product. Working notes : 1. There will be a additional sales revenue of `2,7, if Alternative 1 is chosen. 2. Acceptance of either Alternative 1 or 2 will mean a loss of revenue of `21, from the sale of the obsolete material XY and hence it is an opportunity cost for both of the alternatives. The original purchase cost of `75, is a sunk cost and thus not relevant. 3. Acceptance of Alternative 1 will mean that material A must be replaced at an additional cost of `54,. 4. Acceptance of Alternative 1 will mean diversion of material B from the production of product Z. The excess of relevant revenues over relevant cost for product Z is `18 (`39 `21) and each unit of product Z uses four units of material B. The lost contribution (excluding the cost of material B which is incurred for both alternatives) will therefore be `45 for each unit of material B that is used for converting the obsolete materials into a specialised product. 5. Unskilled labour can be matched exactly to the company s production requirements. Hence acceptance of either alternative 1 or 2 will cause the company to incur additional unskilled labour cost at `3 for each hours. It is assumed that the semi-skilled labour will be able to meet the extra requirements of either alternatives at no extra cost to the company. Hence, cost of semi-skilled labour will not be relevant. Skilled labour is in short supply and can only be obtained by reducing the production of product L, resulting in a loss of contribution of `24 (given) or `6 per hour of skilled labour. Hence the relevant labour cost will be `6 (contribution lost per hour) + `5 (hourly rate of skilled labour) i.e. `11 per hour. 6. It is assumed that for each direct labour of input, variable overhead will increase by Re.1 hence for each alternative using additional direct labour hours, variable overheads will increase. 7. The cost of purchasing the sub-assembly will be reduced by `1,35, if the second alternative is chosen and so these savings are relevant to the decision. 8. The company will incur additional variable costs, of `37 for each unit of material C that is manufactured, so the fixed overheads for material C viz. `18/- per unit is not a relevant cost. Ans. 27: Options Details Manufacturing Sub Contract Amount (` ) Amount (` ) Selling price 1 1 Variable Cost 8 9

42 Contribution 2 1 Fixed Cost 3,92, 1,5, BEP (units) 19,6 15, Ans. 28: Point of Indifference = level of production where both options will have same outcome. It can be calculated as : Difference in Fixed cost = ` (3,92, 1,5,)=` 2,42, Difference in contribution per unit = ` 1 Point of indifference = 2,42, /1 = 24,2 units. It may be calculated in alternative way. Indifference Point (x): (2x 392) = (1x 15) 1x = 242 X = 242 (i) If Market demand is above 15 : manufacture is recommended (ii) For Demand 2421 to 3 units : Manufacture fully in-house. (iii) For Demand 15 to 242 units : Sub-contract Working Notes: Particulars Option I Process L to M Sale of Product M 648, Option II Sell new product A Amount (` ) Amount (` ) Sale of Product A 21 (Less: Revenue lost on Product L ) 4, (Less: Revenue lost on Product J) 35 Less: Additional Cost 18, 84 Incremental Profit Decision : Option II is better by ` 23 Ans. 29: Working Notes: 1. Present demand of components (in batches) from 1,8 (maximum) available machine hours and projected estimates of components demand (in batches) in the next year. Maximum available machine hours 1,8 Machine hours needed to manufacture components. A, B and C (Per batch of ten numbers) of water purifier Components Total A 2 Machine hours B 28 Machine hours

43 C 24 Machine 72 hours Present demand (in batches) of components A, B and C (1,8 hours/ 72 hours) 15 Projected estimate of demand of components A, B and C (add 5% increase) in 225 the next year 2. Present and future fixed costs: Present fixed cost of 15 `2/- per batch 3, Add: Increase in fixed cost to meet 5% increase in demand 1, Total future fixed cost for 225 batches 4, 3. Expected purchase cost of components View point Probability Component A B C Expected price Expected Price Expected Price ` ` ` Pessimistic (`12.25) (`2.25) (`16.25) Most likely (`11.5) (`13.5) (`14.5) Optimistic (`8.25) (`14.25) (`12.25) Total Present contribution (per batch) Selling price (per batch) 8 Less: Variable production cost 32 Less: Variable assembly cost 5 37 Contribution (per batch) 43 Total Present contribution on 15 batches 64,5 ` (i) Maximum number of batches that could be produced in 1,8 machine hours each of the three alternatives namely buying A or B or C is considered respectively. (a) Buy component A (from outside) No machine hour required Make component B 28 Machine hours required Make component C 24 Machine hours required Total 52 Number of batches that could be produced internally batches (1,8 hours/52 hours) (b) Buy component B (from outside) No machine hour required Make component A 2 Machine hours required `

44 Make component C 24 Machine hours required Total 44 Number of batches that could be produced internally batches (1,8 hours/744 hours) But in view of projected (expected) market demand of 225 batches, production would be restricted to 225 batches only. (c) Buy component C (from outside) No machine hours required Make component A 2 Machine hours required Make component B 28 Machine hours required Total 48 Number of batches that could be produced internally 225 batches (1,8 machine hours 748 hours) (ii) Statement of financial implication when purchases of component A, B and C are made from outside(in view of the fact that production capacity will be limited to 5% increase) Component bought A B C ` ` ` Total variable cost per batch (I) Expected purchase cost (II) (Refer to working note 3) Increase I variable cost per batch (III) = (II I) Present contribution per batch (IV) (Refer to working note 4) Revised contribution per batch (V) = (IV III) Total revised contribution 8,791 87,3 91,33 (27.69 batches `389) (225 batches `388) (225 batches `46) Advise: Purchase component C from outside as it gives maximum contribution on manufacturing A and B internally. (iii) Profit Statement (When C is bought from outside and A, B were manufactured internally and extra production is made and sold) Per Batch ` Total (for 225 batches) ` Sales revenue: (I) 8. 1,8, (225 batches `8) Less: Variable costs (`(Per batch) : (II) Production cost of A `64

45 Production cost of B `18 Production cost of D Production cost of E Production cost of C (Refer to working note 3) `344 `24 `8 `14 Assembly cost ` Contribution : (III) (-II) ,35 Less: Fixed costs , (`4, / 225 batches) (Refer to working note 2) Profit (225 batches `394) Ans. 3: The components are made in a machine shop using three identical machines each of which can make any of the three components. Total machine hours required for 3 components = = 15 hours Total capacity of 3 machines is 12, machine hours per month and is just sufficient to meet the current demand. Hence, the current demand is 12,/15 = 8 units of product z per month. Profit made by the company for current month. Sale price 3 Less: Variable cost = 218 Contribution per unit 82 Total contribution 8 x 82= 65,6 Less: fixed cost per month 5, Profit for current month RS. 15,6 (a) From next month onwards, the company expects the demand for z to rise by 25% i.e., 8+25% = 1, units per month. One component should be bought from the market. Which component? Statement of extra cost of component per unit Component A B C Market price Less: Variable cost Extra cost of buying one unit Machine hours required per unit Extra cost per machine hour 16/4= 4 `4 5 15/5=`3 Ranking II I III 6 3/6=`5

46 Because of Ist rank (lowest extra cost), component b should be bought from the market. Also additional capacity generated from component b is 5/1 hours = 5% Manufacturing Hours C 1, units x 6 hours = 6, A 1, units x 4 hours = 4, B 4 units x 5 hours = 2, (Balance) Total 12, Balance 6 units of B should he bought from the market. ( c) Profit made by the company Component Element of cost Cost per unit No. of units Amount(`) A B B C Assembling Total variable cost Add: Fixed cost Total cost Sales 1, units at `3 per unit Profit on 1, units Variable cost Variable cost Market price Variable cost Variable cost , 4 6 1, 1, 48, 24, 45, 8, 3, 2,27, 5, 2,77, 3,, 23, Ans. 31: Demand 52, 48,5 26,5 3, A B C D Direct Material M/c Other Variable Cost Total Variable Cost Selling Price Contribution (`/u) M/s Hours per unit Contribution (`/ M/c hr.) Ranking III II IV I Sub-Contract Cost `/u) Contribution (`/u) on (Sub- Contract) I Division: It is more profitable to sub-contract B, since contribution is higher subcontract. 1st Level of Operations: 1,5, hours, Produce D as much as possible. Hours required = 3, units 3 = 9, hours Balance hours available: 6, hours. Produce the next best (i.e. A, Since B is better outsourced)

47 6, hrs 6 hrs/unit = 1, units of A. 1st Level of Operation: Contribution(units) Contribution (`) A Produce 1, units 18 1,8, A Outsource 42, units 16 6,72, B 48,5 units Outsource fully 3 14,55, C 26,5 units Outsource fully 18 D 3, units Fully produce 18 5,4, Total Contribution: 33,24, Less: Fixed cost 1,, Net Gain 23,24, 2nd Level of Operation: Both A and C increase contribution by own manufacture only by `2/- per unit. 1,5, hrs can produce 25, units of A. Contribution increases by 25, 2 = 5, (Difference in Contribution sub-contract and own manufacturing) = 2 But increase in fixed Cost = 5, At the 2nd level of operation, the increase in contribution by own manufacturing is exactly set up by increase in fixed costs by `5,/-. It is a point of financial indifference, but other conditions like reliability or possibility of the sub-contractor increasing his price may be considered and decision may them but towards own manufacture. 3rd Level Additional: 1,5, hrs available Unit of A that are needed = [52, 25, (2 nd Level) 1, (1 st Level)] = 17, units 6 hrs/u = 1,2, hrs. Balance 48, hrs are available for C to produce 6, units. Increase in Contribution over Level 1st or 2 nd : A: 17, 2 = `34, C: 6, 2 = `12, = `46, Increase in fixed costs = `5, Additional Loss = ` 4, 4 th Level Additional: 1,5, hrs can give 1,5, 8 = 18,75 unit of C. Increase in Contribution 18,75 2 = ` 37,5 Increase in Cost = (` 5,) Level 3rd loss c/fd = (` 4,) Level 1st profit will order by = (` 16,5)

48 Advice: Do not expand capacities; sell maximum No. of units by operating at 1,5, hrs. capacity (level 1st ) and gain `23,24,. Summary: Product Produce Sub-Contract Contribution Contribution Total (Units) (Units) (Production) (Sub-Contract) Contribution A 1, 42, 1,8, 6,72, 8,52, B - 48,5-14,55, 14,55, C - 26,5-4,77, 4,77, D 3, - 5,4, - 5,4, 33,24, Fixed Cost 1,, Profit 23,24, Ans. 32: Calculation of contribution per unit Particulars EXE WYE (a) selling cost P.U Variable cost P.U. Dept. 1 Direct materials 58 1 Direct labour 5 hours 7.5 hours 5 75 Variable overheads (5 hrs*`2.4) 12 - (7.5 hrs*`2.4) - 18 (i) Dept.2 Direct materials Direct labour 9 12 (7.5 hrs*`3.6) 27 - (1 hrs* `3.6) - 36 (ii) Total variable cost (i)+(ii) Contribution P.U. (a)-(b) Calculation of contribution per unit if facilities of Dept.1 were sub-contracted but facilities of Dept.2 used internally (`) Particulars EXE WYE Selling price per unit (a) Cost of sub-contracting Dept.1 facilities Cost of manufacture in Dept.2 internally Total variable manufacturing cost per unit Contribution per unit (a)-(b) Calculation of contribution per unit if facilities of Dept.1 and Dept.2 are sub-contracted Particulars EXE WYE

49 Selling price per unit (a) Cost of sub-contracting P.U. Dept.1 Dept Total variable cost P.U. (b) Contribution P.U. (a)-(b) Statement showing number of units to be produced and sold to earn maximum profit by using own manufacturing capacity Particulars EXE WYE Dept.1 (1,75, hrs/5 hrs) (1,75, hrs/7.5 hrs) Dept.2 (2,8, hrs/7.5 hrs) (2,8, hrs/1 hrs) 35, - 37, ,333-28, Maximum unit can be produced and sold by using facilities of 35, 23,333 both departments. Maximum contribution (35, units* `117) (23,333 units*`165) Les: fixed cost 4,95, ,49,945 (Dept.1 `5,, + Dept.2 `1,,) 15,, 15,, Maximum profit 25,95, 23,49,945 Suggestion: by production and sale of 35, units of EXE is maximum, it is suggestion to manufacture EXE internally. Calculation of profit from EXE Contribution on internally produced units (35, units * `117) Contribution when Dept.1 services were sub-contracted (2,333 units * `99) Contribution when Dept.1 & Dept.2 services were sub-contracted (1,167 units * `87) (`) 4,95, 2,3,967 1,1,529 Total contribution of EXE Less: fixed cost 44,27,496 15,, Profit 29,27,496 Calculation of total contribution of WYE (`) Contribution on internally produced units (23,333 units * `165) 38,49,945 Contribution when Dept.1 services were sub-contracted (4,667 units * `146) Contribution when Dept.1 and Dept.2 services were sub-contracted (35 units * `136) 6,81,382 4,76, Total contribution of WYE 5,7,327 Less: fixed cost 15,, Profit 35,7,327 Suggestion: profit is maximum for product WYE. Hence 31,5 units of WYE should be produced to yield a sum of `35,7,327 as profit. Ans. 33: Working notes: 1. (a) Total normal and overtime hours available. Department A B

50 Normal capacity hours 6 52 Overtime hours 3 26 (5% of normal hours in each department) Total available hours 9 78 (b) Total hours required to meet fully the market demand of 2,5 units of P and 2, units of Q. Hours required for manufacturing P 2,5 units of Product Hours required for manufacturing Q 2, units of Product A Department B 25 5 (2,5 Units.1 hour) (2,5 Units.2 hour) 6 4 (2, Units.3 hour) (2, Units.2 hour) Total hours required Sub-contracting should be resorted: To meet the market demand of 2,5 units of product P and 2, units of product 85 and 9 hours [Refer to working note 1(b)] are required in departments A and B respectively. In department B only 78 hours are available and thus does not meet fully the requirement of 9 hours. Hence, sub-contracting should be resorted to meet the market demand fully. 3. (i) Contribution per unit; Product P Q Normal hours Overtime hours Normal hours Overtime hours Director material cost (`) Direct labour cost Dept. A (`) (`1.1 hr.) (`15.1 hrs.) (`1.3 hrs.) (`15.3 hrs.) Dept. B: (`) (`12.2 hrs.) (`18.2 hrs.) (`12.2 hrs.) (`18.2 hrs.) Total variable cost per unit (`) : (A) Sub-contract price per unit (`) : (B) Contribution / cost saving / (Loss per unit (`) (1.1) (C) = [(B) (A)] (ii) Contribution per hour

51 Hours required per unit Dept. A Dept. B Contribution hour per Dept. A (`) Loss (`4.6/.1 hrs.) (`2.9/.1 hr.) (`1.6/.3 hrs.) -- Dept. B (`) Loss (`4.6/.2 hrs.) (`2.9/.2 hr.) (`1.6/2. Hrs.) Utilization of normal and overtime available hours to meet fully monthly market demand of 2,5 units of P and 2, of Q. (i) An analysis of contribution statement (Refer to working note 3) clearly shows that 2,5 units of the product P should be manufactured by utilising the normal capacity hours of departments A and B. The manufacturing of 2,5 units of P will consume 25 normal hours of department A and 5 hours of department B (Refer to working note 1(b). (ii) For manufacturing 2, units of product Q, it is beneficial to utilise the remaining normal available hours of departments A and B. The normal available hours in the department B are only 2 hours, [52 hours 5 hours] and in department A 35 hours [6 hours 25 hours]. 1 units of product Q can be manufactured by utilising the normal available hours of departments A and B. The manufacturing of 1 units of Q in normal available hours will utilise 3 hours in department A and 2 hours in department B. Alternative to 4 (i) & (ii) (By Linear Programming) Let x & y be the no. of units produced of Products P & Q respectively, utilizing normal time in both departments. Maximize, Z(Savings) = 4.6x + 1.6y s.t.c.,.1x +.3y 6 [Department A Normal Time].2x +.2y 52 [Department B Normal time] x 25 [Maximum Demand of Product P] y 2 [Maximum Demand of Product Q] x, y For line,.1x +.3y = 6 x 6 y 2 For line,.2x +.2y = 52 x 26 y 26

52 ABCDE is feasible region Points Coordinates Value of Objective Function A, 2 32 B 9, C 25, D 25, 115 E, Z max = 1166 when x is 25 and y is 1 (iii) Now for manufacturing the remaining 1,9 units of product Q, we have 32 normal hours plus 3 overtime hours in department A and 26 overtime hours in the department B. The manufacturing cost per unit of product Q comes to `11.6 when normal hours of department A and overtime hours of department B are utilized. {`5 (Material Cost) + `3 (Direct Labour in Department A) + `3.6 (Direct Labour in Department B)} On comparing `11.6 with sub-contracting price of `12 per unit, we arrive at a contribution of.4 per unit. Hence maximum number of units of product Q should be manufactured by using normal hours of department A and overtime hours of department B. since.3 and.2 hours are required respectively for manufacturing one unit of product Q in the two departments, therefore, utilising 32 normal hours and 213 overtime hours in departments A and B respectively, units (or say 1,67 units) of product Q are manufactured. (iv) Finally, to manufacture remaining 833 units of Q, the available time is 3 overtime hours and 47 overtime hours in department A and B respectively. According to (working note 1) the available time in department B is short by 12 hours (9 required hours 78 available hours) therefore 833 units of Q cannot be made

53 internally. But few units can be made by utilising the available overtime hours in departments A and B. The manufacturing cost of 1 unit of Q by utilizing overtime hours in departments A and B comes to `13.1 (Refer to working note 3) which on comparison with subcontract price of `12 gives rise to a situation of loss of `1.1 per unit {`13.1 `12}. Hence it is advisable not to manufacture the remaining 833 units internally. These 833 units should be sub-contracted at a price of `12/- per unit. (i) Statement of quantity of each product to be manufactured / or to be sub-contracted for fulfilling the market demand in most economical way. (ii) Available hours (Refer to working note 1(i) Departments A B Normal time hours Overtime hours Normal time hours Overtime hours Production 2,5 units of P (Refer to working note 4 (i)) (2,5 units.1 hrs.) (2,5 units.2 hrs.) 1 units of Q (Refer to working note 4 (ii) (1 units.3 hrs.) (1 units.2 hrs.) 167 units of Q (Refer to working note 4(iii)) (1,67 units.3 hrs.) (1,67 units.2 hrs.) Statement Showing Total Cost (Based on the solution in (i) above) Products Particulars P Q Sub contract Total price ` ` ` ` Direct Material Cost 25, 5,835-3,855 (2,5 units (1,167 units `5) `1) Direct Wages: Dept. A 2,5 3,5 -- 6, (25 hours (35 hours `1) `1) Dept. B 6, 4, ,75 (5 hours (2 hours ` hours `18 `12) Fixed overhead 18, 6,4-24,4 Cost of ,996 9,996 `12 per unit on subcontracting Total Cost 51,5 19,89 9,996 81,35 Ans. 34: (a) Calculation of Optimum Production Mix

54 Evaluation of Limiting factor: Particulars Material Hours in Department A Hours in Department B Required : X 14,8 kgs. 3,7 hours 2,96 hours Y 2, kgs. 3, hours 4,5 hours Total Requirement 34,8 kgs. 6,7 hours 7,46 hours Available resources 17, kgs. 3,4 hours 3,64 hours Shortage 17,8 kgs. 3,3 hours 3,82 hours Hence all the three resources are limiting factors. Statement showing ranking Particulars Product X Product Y Sales 9 8 Less: Direct Material Dept. A Dept. B Contribution p.u Contribution per kg. of raw material Rank I II Contribution /hr. of Dept. A Rank II I Contribution /hr. of Dept. B Rank I II Let x 1 and x 2 donate quantities of product X and product Y respectively. Maximize, Z(Contribution) = 36x 1 +31x 2 s.t.c., For material, 2x1 + 2x2 17, For Dept. A,.5x1 +.3x2 3,4 For Dept. B,.4x1 +.45x2 3,64 Demand constraint, x1 7,4 and x2 1,

55 12, x1 +2x2 = 17.5x1 +.3x2 = 34.4x1 +.45x2 = 364 x1 = 74 x2 = 1 1, 85 8, , 68, 91, ABCDE is feasible region Points Coordinates Value of Objective Function A, B 37, C 425, D 68, 2448 E, Z max = when x is 425 and y is 425 Therefore, optimum product mix = X 4,25 units and Y 4,25 units. (b) Statement showing product with higher contribution

56 Product Maximum Demand (a) Maximum Production by Dept A (b) Maximum Production by Dept B (c) Maximum Production with available materials Feasible Maximum production (lower of a, b, c and d) Contrib -ution X 7,4 6,8 9,1 8,5 6,8 2,44,8 Y 1, 11,333 8,88 8,5 8,88 2,5,728 Therefore, Product Y should be produced at 8,88 units resulting in a contribution of `2,5,728. Ans. 35: Working Notes: 1. FOB price of dismantled kit: FOB price of dismantled kit (in$) 51 FOB price of dismantled kit (in `) 24, ($51 `47.59) 2. Cost of a dismantled kit to Z Inc. If `12 is the S. P. of kit to Z Inc. then its C `1 Re 1 Rs.1 = Rs.12 If `24, is the S. P. then C. P. is Rs.1 = `24, Rs.12 = `2, 3. Cost of local procurements: 14% of the supplies made by Z Inc. or 14% `1,* = `14, *Being 5% of cost of a dismantled kit to Z Inc. 4. Landed cost of a dismantled kit: ` FOB price 12, (5% `24,) (Refer to working note 1) Add: Insurance & freight 5 CIF price 12,5 Add: Customs duty 3,75 (3% `12,5) Landed cost of a dismantled kit 16,25 5. Cost of the standard items procured locally: 48% of the cost of locally procured goods

57 = 48% `14, = `6,72 6. Royalty payment per computer: Let x = Selling price per unit of personal computer y = Royalty paid per computer Since 2% is the margin of profit on S.P. it main a margin of 25% on C.P. Therefore we have X = 1.25 (`32,25+ `15 + y) Y = 1% {x (`6,72 + `16,25)} On solving the above equations we get: X = `43, Y = `23.43 or `2, (Approx) Statement showing the selling price of a personal computer in India ` A. Landed cost of a dismantled kit (Refer to working note 4) 16,25 B. Cost of local procurement (Refer to working note 3) 14, C. Cost of assembly and other overheads per computer 2, D. Total cost of manufacture: (A+ B + C) 32,25 E. Technology fee per computer 15 (`3,,, / 2,, computer) F. Royalty payment per unit (Refer to working note 6) G. Total cost (D + E+ F) 34,4 H. Profit (2% on selling price of 25% of total cost) 8,6 I. Selling price (per computer) 43, Ans. 36: (a) Contribution per tin = Selling Price Variable cost = 21 ( ) = `8 per tin. Loss on operation: Fixed cost per annum = 2,, units 4 per unit = 8 lakhs Fixed cost for 1 quarter = 8/4 = 2 lakhs ` Fixed cost for the quarter 2,, Less: Contribution on operation (8 1,) 8, Expected loss on operation (1,2,) Loss on shut down: `

58 Unavoidable Fixed Cost 74, Additional shut down cost 14, Loss on shut-down (88,) Conclusion: Better to shut down and save `32,. Shut-down point (number of units) = Avoidable Fixed Cost Contribution per unit = (2,, 88,)/8 = 14, units. Ans. 37: Statement of cost per tonne and net profit earned in respect of each factory Lucknow Pune Present production tonnes: (A) 7,2 1,8 Rs. Rs. Cost of raw material (Rs. in lacs) (Refer to working note 1) Other variable costs (Rs. in lacs) Fixed cost (Rs. in lacs) Total cost (Rs. in lacs): (B) Cost per tonne (Rs) : (C) = [(B) / (A)] 1,38 1,345 Selling price (Rs. Per tonne: (D) 1,45 1,46 Net profit per tonne (Rs.) : [(D) (C)] Total net profit (Rs. in lacs) (Rs.7 7,2 tonnes) (Rs.115 1,8 tonnes) Total profit of the company = Rs lacs (Rs.5.4 lacs + Rs lacs) Alternative production plan to earn optimum Lucknow Pune Maximum production capacity (tonnes) 9, 11,88 Present production (tonnes) 7,2 1,8 Rs. Rs. Cost per tonne of output: 8 81 Cost per tonne of output manufactured from locally purchased raw material: (A) (Refer to working note 2) Cost per tonne of output manufactured from material purchased from Bhopal : (B) (Return to working note 3) Other variable cost (Rs.) : (C) Rs Lacs Rs Lacs 7,2 tonnes 1,8 tonnes Selling price per tonne (Rs.) : (D) 1,45 1,46

59 Contribution per tonne of Output : [(D) {(A)+(C)}] Contribution per tonne of Output : [(D) {(B)+(C)}] (When material was purchased from Bhopal) The priority to produce 18, tonnes of total output is as below as apparent from the above data: Pune factory (Local purchase of raw material) Lucknow factory (local) purchase of raw material) Pune factory (raw material purchased from Bhopal) Lucknow factory (raw material purchased from Bhopal) Suggested alternative production plan : Production priority Raw Material Output (in tonnes) Priority 1 st 2 nd Input(in tonnes) Lucknow Pune Total I 11,7 tonnes 13, -- 11,7 11,7 II 5,4 tonnes 6, 5,4 -- 5,4 III (11,88 11,7) = 18 tonnes IV 72 tonnes balancing figure (18, 17,28 tonnes) Working Notes: 3 rd 4 th , 6,12 11,88 18, Lucknow Pune 1. Present production output (tonnes) 7,2 1,8 Total raw material required for present production (tonnes) 8, 12, 1 1 7,2 1,8 9 9 Raw material produced locally (tonnes) 6, 12, Raw material product from Bhopal 2, -- Cost of raw material purchased locally and from Bhopal (Rs. in lacs) 2. Cost per tone of output manufactured from locally purchased raw material (in Rs.) 3. Cost per tonne of output manufactured from material purchased from Bhopal (in Rs.) (Rs.72 6,+ Rs.792 2,) (12, Rs.729)

60 Ans. 38: (i) (a) Statement showing apportionment of joint costs sales value at split-off Products Sales in tones (a) Selling price per ton (`) (b) Sales value (`) (c) = (a) * (b) Apportioned cost (`) Caustic soda 2,4 1 2,4, 1,, Chlorine 1,6 15 2,4, 1,, Total 4,8, 2,, joint *Apportioned joint cost = Total joint cost * sale revenue of each product. Total sale value Apportioned joint cost to caustic soda = `2,, * `2,4, = 1,, `4,8, Apportioned joint cost to chlorine = `2,, * `2,4, = `1,, `4,8, (b) Statement showing apportionment of joint costs on physical measure (tons) Products Sales in (tons) Apportioned ** joint costs (`) Caustic soda Chlorine 2,4 1,6 1,2, 8, Total 4, 2,, **Apportioned joint cost = Total joint cost * sales of each product (tons) Total sales (tons) Joint cost apportioned to caustic soda = `2,, * 2,4 tons = `1,2, `4 tons Joint cost apportioned to PVC = `2,, * 1,6 tons = `8, `4, tons (c) Statement showing apportionment of joint costs by using estimated net realizable value method Products Sales revenue (`) Further pro-cessing Net realizable value Apportioned ** joint cost (`) (`) cost (`) Caustic soda (2,4 2,4, tons * `1) PVC (1, tons of 4,, - 4, 2,4, 3,6, 8, 1,2, PVC * `4) Total 6,, 2,, ***Apportioned joint cost = Total joint cost * Net realizable value of each product. Total net realizable value Apportioned joint cost for caustic soda = `2,, * `2,4, = `8, `6,, Apportioned joint cost for chlorine = `2,, * `3, 6, = `1, 2, `6,, (ii) Statement of gross margin percentage of caustic soda and PVC under sales value at split off: physical measure (tons) and estimated net realizable value method

61 Caustic soda Sale revenue : (A) Joint cost allocated : (B) Gross margin (C) : (A)-(B) Sale value at split off (`) Physical measure (tons) (`) Estimated net realizable value (`) 2,4, 1,, 1,4, 2,4, 1,2, 1,2, 2,4, 8, 1,6, Gross margin (%) (C) * 1 (A) (b) PVC: Sales revenue (A) Joint cost allocated Further processing cost Total cost Gross margin (c) : (A)-(B) 58.33% 4,, 1,, 4, 1,4, 2,6, 5% 4,, 8, 4, 1,2, 2,8, 66.67% 4,, 1,2, 4, 1,6, 2,4, Gross margin (%) (C) *1 (A) 65% 7% 6% (iii) Consequence of the operating income of inorganic chemicals for November, 1998 by accepting the offer of daily swimming pools Ltd. to purchase, 1,6 tons of chlorine Incremental revenue (loss) due to processing of chlorine to PVC (`1, 6,) (1,6 tons * `15) (1, tons * `4 tons) Saving on further processing cost of chlorine into PVC 4, Incremental operating income (`1, 2,) The operating income of inorganic chemicals will be reduced by `1,2, in the month of November, 1998 if it accepts the offer of daily swimming pools Ltd., to purchase 1,6 tons of chlorine in November, 1998 at `15 per ton. Ans. 39: Option I Units Produced 1 Less: Defective (4%) 4 Unit Sold 96 Sales 8 ) 768 Less: Variable cost of Production 5 ) 5 Less: Inspection of finished goods 1 Spare part replacement cost 4 (4 defective 2 per 2 defective) Profit 254 Option II Units Produced 1 1 Less: Warranty Replacement (1% of unit sold) Unit Sold Sales 8 ) 792 Less: Variable cost of Production Units sold 5) Warranty Replacement 5) Less: Machine setup cost 8

62 Profit Hence option II is more beneficial from financial perspective. Ans. 4: (i) Comparative Statement of cost for purchasing from Y Co Ltd under current policy & JIT Particulars Current Policy JIT Rs Rs Purchasing cost 18,2, 18,2,26 (13, 14) (13, 14.2) Ordering cost (2 13 orders) (2 13 orders) Opportunity carrying cost 1,5. 1,5.15 (1/ %) (1/ %) Other carrying cost(insurance, material handling etc) 1, (1/ ) Stock out cost 2 (4 5) Total relevant cost 18,32,76 18,21, Comments: As may be seen from above, the relevant cost under the JIT purchasing policy is lower than the cost incurred under the existing system. Hence, a JIT purchasing policy should be adopted by the company. (ii) Statement of cost for purchasing from Z Co Ltd. Particulars Rs. Purchasing cost 1,76,8 (13,x13.6) Ordering Cost 26 (2x13 orders) Opportunity Carrying 12 Cost (1/ %) Other Carrying Cost 15 (1/2 1 3.) Stock out Cost 2,88 (8x36) Inspection Cost 65 (13, x.5) Customer Return Cost 6,5. ( 13, x 2% x 25) Total Relevant Cost 1,87,342 Comments : The comparative costs are as follows, Under current policy Rs 18,32,76. Under purchase under JIT Rs 18,21,925.1 Under purchase from Z Co Ltd Rs 1,87,342. Packages should be bought from Z Co as it is the cheapest. Ans. 41: Let x 1 and x 2 be the amount to be invested in first and second stock portfolio respectively. The average rate of return for first portfolio is 1% and for second portfolio, it is 2%. Since the company wishes to maximize the return from investment, the objective function is as given below: Maximise Z =.1x 1 +.2x 2

63 The maximum amount available for investment is `1,,. Hence, x 1 + x 2 1,, (1) Further, the maximum investment allowed in either portfolio set is `75,. Therefore, x 1 75, (2) and x 2 75, (3) The first portfolio has a risk rating of 4 (on a scale from to 1) and the second has 9. The company will not accept a risk factor above 6. Therefore, 4x 1 + 9x 2 6 (x 1+x 2) (4) Further, the company will not accept an average rate of return below 12%. Hence,.1x x 2.12 (x 1 + x 2) (5) Also, x 1 and x 2 (6) The linear programming model for the given problem can now be formulated as follows: Maximise Z =.1x 1 +.2x 2 Subject to the constraints x 1+x 2 1,, (1) x 1 75, (2) x 2 75, (3) 4x 1 + 9x 2 6 (x 1 + x 2) or 2x 1 + 3x 2 (4).1x 1 +.2x 2.12 (x 1+x 2) or.2x 1 +.8x 2 (5) where x 1, x 2 The problem is solved graphically below: The point of intersection for the lines - 2x 1 + 3x 2 = and x 1 + x 2 = 1,, is given by B (6,, 4,)

64 The point of intersection for the lines X 1 = 75, and x 1 + x 2 = 1,, is given by C (75,, 25,) Similarly, the lines x 1 = 75, and.2x 1 +.8x 2 = intersect at point D (75,, 18,75) Thus, the feasible region is bounded by ABCDA and feasible points are A (, ); B(6,, 4,); C(75,, 25,) and D(75,, 18,75). Value of the objective function at the above mentioned feasible points is calculated below: At A, Z= At B, Z=.1 6, +.2 4, = 6, + 8, = `14, At C, Z=.1 75, , = 7,5 + 5, = `12,5 At D, Z=.1 75, ,75 = 7,5 + 3,75 = `11,25 We find that the value of the objective function is maximum (`14,) at point B(6,, 4,). Hence, the company should invest `6, in first portfolio and `4, in second portfolio to achieve the maximum average rate of return of `14,. Ans.42: Under the usual notations where S1, S2, S3 are stock Variables, A4 = the artificial variable S4 = Surplus Variable We have, Max. Z = 1x 1 + 8x 2 + S 1 + S 2 + S 3 + S 4 M A 4. S.t. 3x 1 + 5x 2 + S 1 = 15 x 2 + S 2 = 2 8x 1 + 5x 2 + S 3 = 3 x 1 + x S 4 + A 4 = 25 x 1 x 2 S 1 S 2 S 3 S 4 A 4 Basis C B C j M

65 S S S A 4 - M Z j - M - M M -M -25M C j-z j 1+M 8+M -M Ans. 43: (i) Simplex Table Basis C j 8 6 C B X 1 X 2 S 1 S 2 X 1 X 2 Z j NER 8 6 C j - Z j /3-1/6 5/3-5/3-1/6 1/3 2/3-2/3 Note: Z j values are obtained by multiplying each row with cost and adding the values of the respective column as under: X 1 X 1 X 2 S 1 S = 8 8 = 8 1/3 = 2.2/3 8-1/6 = -1.1/3 X 2 6 = 6 1 = 6 6-1/6 = /3 = 2 Adding Z j 8 6 5/3 Net evaluation Row (NER) is obtained by deducting Z j from C j as under: 2/3 8-8 = 6-6 = - 5/3 = -5/3-2/3 = -2/3 Since the values of NER are, the solution represented by this tableau is optimal. (ii) Product Hours Co-efficient of Contribution NER ` S 1 S 2 M I X 1 6 5/3-1 M II X /3 _32 Total optimal contribution 132 Since the values of NER ar e, the solution represented by this tableau is optimal. Ans. 44: (i) The solution is optimal, since all the elements in the last row (Zj-Cj) are non-negative. Information has been provided for Zj-Cj & not Cj-Zj

66 (ii) No, because the elements in the last row under non-basic variables x 1 and s 1 are strictly positive. (iii) No, because quantity of none of the basic variables x 2 or s 2 is zero. (iv) Yes, artificial variable doesn t exist in final solution. (v) Machine A is being used to the full capacity because the quantity value of variable s 1 is zero in the optimum simplex table. This indicates that the entire time (in hours/week) is consumed by the activities of the model. (vi) From the given table, the element in the last row under x 1 is 1; therefore, an increase of x 1 from its current zero level to a positive level will mean the reduction in the total profit at the rate of unity per week. Hence in order to ensure that there should not be any reduction, price of x 1 should be increased by ` one. (vii) Profit will get reduced by 2hrs. 5p.h. = ` 1 (viii) x 1= and x 2 = 1 with total profit of ` 5. Ans. 45: Type I II III Total no. of 2-seater 8-seater 5- seater Passengers Vans Big Cars Small Cars Route I Residence H.O Residence Route II Residence Br. Residence No. of Vehicles Max. capacity No. of Passengers 26 Let i be the ith route And j be the type of vehicle, so that S 11 = no. of vans (vehicles on route I, type I) S 12 = no. of 8 seater cars on route I S 13 = no. of 5 seater cars on route I S 21 = no. of vans-on route II S 22 = no. of 8 seater cars on route II S 23 = no. of 5 seater cars on route II Objective: Cost Z = 6 S S S S S S 23 2 S S S 13 = 18 2 S S S 23 = 4 S 11 +S 21 < 4 S 21 + S 22 < 1 S 31 + S 32 < 2 All Sij >

67 Ans. 46: Primal Minimize, Z = 4x1 5x2 + 6x3 Subject to the constraints 3x1 + 2x2 + 4x3 9 2x1 + 3x2 + 2x3 5 7x1 + 2x2 + 4x3 1 6x1 3x2 + 4x3 4 2x1 + 5x2 3x3 3 2x1 5x2 + 3x3 3 x1, x2, x3 Dual Maximize Z = 9y1 + 5y2 1y3 + 4y4 + 3y5 3y6 Subject to constraints 3y1 + 2y2 7y3 + 6y4 + 2y5 2y6 4 2y1 + 3y2 + 2y3 3y4 + 5y5 5y6 5 4y1 + 2y2 + 4y3 + 4y4 3y5 + 3y6 6 y1, y2, y3, y4, y5, y6 By substituting y5 y6= y7 the dual can better be expressed as: Maximize, Z = 9y1 + 5y2 1y3 + 4y4 + 3y7 Subject to constraints 3y1 + 2y2 7y3 + 6y4 + 2y7 4 2y1 3y2 2y3 + 3y4 5y7 5 4y1 + 2y2 + 4y3 + 4y4 3y7 6 y1, y2, y3, y4, y7 unrestricted in sign. Ans.47: The given problem is an unbalanced transportation problem since the availability of trailers (= =25) is less than the requirement (= =35). Therefore, it is first converted into a balanced problem by adding a dummy terminal with an availability of 1 trailers and cost elements for various plants as zero. The problem becomes as given below. Plants Terminals A B C D Availability U V W X

68 Dummy 1 Requirement The objective of the company is to minimize transportation cost. To achieve this objective, let us find an initial feasible solution by applying Vogel s Approximation Method to the above matrix. Plants Terminals A B C D Availability Difference U /4/1/ 1/1/8/8 V / ///- W / 1/1/15/15 X / 5/5/5/5 Dummy 1 1/ /-/-/- Requirement 13/3/ 1/6/ 6/ 6/1/ Difference The initial solution is as given below which is tested for optimality. Plants Terminals A B C D Availability U V W X Dummy 1 1 Requirement

69 The number of allocation is 7 which is one less than the required m+n-1 (=8) allocations. Introduce a very small quality e in the least cost independent cell (Dummy, B. Let us also introduce u j, v j; I- (1,2 5) j = (1,2,3,4) such that ij = cij-(u1+v j) for allocation cells. We assume that u1= and remaining u i s, v j s and ij s are calculated as below: Terminals A B C D u i s U 3 +θ θ V 2 4 -θ θ W X Dummy 1 -θ e +θ vj s Since some of the ij s are negative, the above solution is not optimal. Introduce in the cell (V,D) with the most negative ij an assignment θ. And the reallocated solution as obtained from above is given below. The values of u i s and v j s and ij s also calculated. Terminals A B C D u i s U V W X Dummy v j s Since all Ij s for non basic cells are positive, therefore, the solution obtained above is an optimal one. The allocation of terminals to plants and their cost is given below. Terminal Plant Cost

70 U A 4 `2 = `8 U C 6 `1 = `6 V B 3 `2 = `6 V D 1 `2 = `2 W B 6 `35 = `21 X D 5 `25 = `125 = `555 Ans. 48: Cost Matrix (Production + Shipping Cost) A 1 A 2 A 3 A 4 A 5 F F F Contribution Matrix (Selling Price-Cost Matrix) A 1 A 2 A 3 A 4 A 5 F F F Minimisation Matrix. (Subtract each element of the above matrix from the largest element) A 1 A 2 A 3 A 4 A 5 Supply F F F Demand This is not a balanced transportation matrix. Hence add a dummy agency A 6s with demand 5 and zero for costs. A 1 A 2 A 3 A 4 A 5 A 6 Supply F F F Demand Incorporating condition (a) of (ii), the 4 units are compulsory and can go out of the minimization effort. Consequently,

71 A 1 A 2 A 3 A 4 A 5 A 6 Supply F F F Demand Condition (b) needs to be tackled while allotting the quantities using the least cost differences. A 1 A 2 A 3 A 4 A 5 A 6 Diff. F F F Diff Step (I) allot 75 units to least cost cell F 3 A 3 since 4 is the max difference. Step (II) allot 5 units to least cost cell F 2 A 6 since 3 is the max. difference. Step (III) allot 45 units to least cost cell F 2 A 4 since 5 is the max. difference. Step (IV) Max. difference has a tie at 2. Hence allot 6 units to least cost cell F 1 A 2 Step (V) Max. difference has a tie between F 1 A 1 and F 1 A 1. Choose F 3 A 1 with least cost. But as per condition. (b) of (ii) we can allot only 3 units instead of 5. Next, F 3 A 1 is given the balance possible demand is 5 units. This also exhausts supply F 3 Step (VI) only F 1A 5 is left out. Hence allot 2 to finish the supply. Step (VII) Allot 15 to F 2 A 5 and obtain the b initial solution by VAM. A 1 A 2 A 3 A 4 A 5 A 6 F F F (iii) The initial solution does not have F 2 to A 1 as a possibility. It is not likely to appear in the final solution also, since in the contribution matrix, it is the worst or in the cost matrix the worst with highest cost. Hence it is like eliminating a prohibited route with high cost M. Therefore, floods or not, this route will not impact the solution. Ans. 49: ij Values are given for unallocated cells. Hence, no. of allocated cells = 5, which = = no. of columns + no of rows 1. Allocating in other than ij cell. Factory S1 D2 D3 Supply

72 This solution is optional since ij are non-ve. For the other optional solution, which exists since ij = at R 3 C 1, this cell should be brought in with a loop: R 3, C 1 R 1 C 1 R 1 C 3 R 3 C 3 Working Notes: Step I : R 1 C 1 (Minimum of 3, 5) Step II : R 2 C 2 (Minimum of 3, 4) Step III : R 1 C 2 balance of C 2 total: 1, R 1 Total = 1 Step IV : R 1 C 3 1 (balance of C 3 total = 2) Step V : R 3 C 3 2 Solution I Solution II Solution I Solution II Cost: 3 х 3 = 9 3 х 2 = 6 4 х 1 = 4 4 х 1 = 4 4 х 1 = 4 4 х 2 = 8 6 х 3 = 18 6 х 3 = 18 5 х 2 = 1 5 х 1 = 5 4 х 1 = 4 Minimum Cost Ans. 5

73 (given) T T T T T (Dummy) Junction values at dummy = 3. 3 was the minimum uncovered element. Previous step was (i) At step II the matrix was: (ii) For Operator I, Most difficult task will be indicated by hours = T 2 Operator II T 2 Operator V T 2 (iii) Most efficient operator = Operator 4 (iv) If the Manager s mistake was not known, We continue the assignment, T 1 5, T 2 4, T 3 3 are fixed. Between T 4 and T 5, 1 or 2 Can be allotted. So, other 1 or 2 Can be denied the job.

74 (v) Although it is always better to start afresh, but, the Manager can go ahead with the optimal assignment as well. Since logically, assignment problem can be solved even without introducing dummy row/column, although it is un-recommended. Ans. 51: Since the Executive Director of the 5 star hotel is interested in maximizing the revenue of the hotel, therefore, the objective of the given problem is to identify the preferences of marriage parties about halls so that hotel management could maximize its profit. To solve this problem first convert it to a minimization problem by subtracting all the elements of the given matrix from its highest element which is equal to ` 1,. The matrix so obtained which is known as loss matrix is given below: Loss matrix/hall Marriage party A 1 X X B C D 2 X X Now apply the assignment algorithm to the above loss matrix. Subtracting the minimum element of each column from all elements of that column, we get the following matrix. Loss matrix/hall Marriage party A 1 X X B 2 3 C 3 2 D 2 X X The minimum number of lines to cover all zeros is 3 which is less than the order of the square matrix (i.e. 4), the above matrix will not give the optimal solution. Subtracting the minimum uncovered element (= 1) from all uncovered elements and add it to the elements lying on the intersection of two lines, we get the following matrix Marriage party A X X B 3 3 C 4 2 D 1 X X Since the minimum number of lines to cover all zeros is 4 which is equal to the order of the matrix, the above matrix will give the optimal solution which is given below: Marriage party

75 A X X B 3 3 C 4 2 D 1 X X and the optimal schedule is : Revenue (`) Marriage party A Hall 2 9, B Hall 3 8, C Hall 4 8, D Hall 1 1, Total 35, Ans. 52: (i) There are 5 rows and 4 columns hence insert a dummy column R5. 1. C2 has been allocated to R1 2. C4 has been allocated to R2. Hence the assignment is restricted to R3 R4 R5 C C C Column Minimum R3 R4 R5 C1 C3 2 3 C5 2 1 R3 R4 R5 C1 1 C3 1 2 C5 1 Hence C1 has been allotted to R3, C3 to R5 to R4. Hence the Minimum cost is = = 54 Lacs (ii) C 3 should give any discount greater than 1 lacs (because co. will bear penalty of ` 1 lac if R 3 is assigned to C 3 ) (iii) Minimum rate of Discount (54-5) = 4/54 = 7.41% Ans 53:

76 E =1 L =1 E = 3 D L = 5 5 K E =11 E =5 1 L =11 L = 8 A J E= 3 2 L E =16 L= E 5 L =16 B 1 4 E= 4 H I L= E= 8 C 3 F L= 8 G 6 (i) (ii) (iii) E=7 L=1 The required network for the given project is drawn above. The critical path of the project is B H J K L and its duration is 16 days. The three types of floats viz total, free and independent floats for various activities of the given project have been calculated in the following table : Floats Activity Duration Earliest Latest Earliest Latest total Free I ndependent Start time Start Time Finish Finish (LST-EST) (Total (F.F.- Stock of tail event) (EST) (LST) Time Time or Float- (EFT) (LFT) (LFT-EFT) Slack of Head Event) A B C D E F G ` H I J K

77 L Ans. 54: Critical Path B C F G I (ii) Calculation of Expected Time, Standard Deviation and Variance of Activities Activity Expected Time Standard Deviation Variance σ² t t = t m +t p t s = p -t 6 6 A (1-2) B (1-3) C (3-4) D (3-5) E (2-6) F (4-7) G (6-8) H(5-9) I (8-1) = = = = = = = = = = = = = = = = = 6

78 (iii) S.D. of Critical Path = Total of variance of Critical Activities = = (iv) (v) Probabilities of completion of job in 27 days. X = 27 Days Z = = For Z = the probability is.5 from the table of area under normal curve or 5%. For 95% of area the corresponding Z value is 1.64 (from the table). Therefore, X = X = = 31 Days (approx.) Ans. 55: (a) (i) Net work diagram (ii) Total floats Critical Path is = 32 weeks Associated Cost = = 582 Activity Duration weeks Early start Latest start Early finish Latest finish Total float

79 (iii) Calculation of crashing Activity Nt Nc Ct Cc Slop = (Cc-Nc) / (Nt-Ct) The critical path activities are Slope Two activities cost slope cost is minimum (2-5 and 5-6) but activity 5-6 is common and critical, it also continuing so reduce by 2 weeks, then reduce activity 2-5 by one week. Activity From-to Project durations Cost I weeks 32-2 = (2 45) + (3 5) = 581 II = (1 45)+(29 5) = 585 After this reduction now two paths are critical = 28 and = 28 So Slope cost =95 7 As cost per week for every alternative is greater than Rs.5 (overhead cost p er week). Therefore, any

80 reduction in the duration of project will increase the cost of project completion. Therefore, time for projects is 29 weeks, minimum cost is Rs.585. Ans. 56: (i) Critical path days Paths: Normal Crash Crash Activity Days, Cost Step I II III IV V VI 1 2 & (4 + 2) Revised critical paths : VII 1 2 & 3 4 (4 + 8) But VII is not done if indirect cost = 7, which is < days (ii) Project duration is 31 days and cost of crashing is 3. Workings of Crashing:

81 Critical path: (37 days) crashing cost. (1) day 4 (2) day 4 (3) days 1 (4) day 6 (5) 1-2 & day (4+2) 6 3 Revised critical path: Duration 31 days (Note: After each crashing a networking diagram has to be drawn and critical path has to be decided). Alternative Solution: (i) Network Diagram:

82 Project duration 37 days Critical Paths: (i) (ii) Crashing by steps Step crash Crashing Crash cost Crashing cost Activity No. of days per day (`) ` Step Step Step Step (i) Network Diagram: Effective Crashing days = 7 Critical paths: (i) (ii) (iii) Project duration = 3 days Crashing cost = ` 36

83 (ii) For optimal project duration, we have to consider indirect cost per day i.e. ` 7. The crashing cost of activity 3-4 is ` 8 which is higher than indirect cost per day. Hence, we may opt it output (step 4). In that case, project duration = 31 days Crashing cost ` 28 Savings in indirect cost = 6 ` 7 = ` 42 Ans. 57: From the frequency distribution of arrivals and service times, probabilities and cumulat ive probabilities are first worked out as shown in the following table: Time between arrivals Frequency Probability Cum. Prob. Service Time Frequency Prob. Cum. Prob Total 1 1 The random numbers to various intervals have been allotted in the following table: 1. Time between arrivals Probability Random numbers allotted Service Time Probability Random numbers allotted Simulation Work Sheet Random Number Time till next arrival Arrival Time a.m. Service begins a.m. Random number Service time Service Ends a.m. Clerk Waiting time Customer waiting Time Time spend by customer in system Length of waiting line

84 Average queue length = Number of customers in waiting line Number of arrivals = = Average waiting time per customer = = minutes Average service time = = minutes Ans. 58: 5, units 2, units Material 1,5, 6,, Direct Labour 1,, 2,56, Refer to W Note i Variable Overhead 5, 2,, Total Variable Cost 3,, 1,56, Fixed Cost 1,5, 1,5, Total Cost 4,5, 12,6, Total cost / unit Sales 1 5, 5,, 5,, 15, x(assumed selling price) 15, x (Total Sales less Total Cost) = Profit 5, 15, x 7,6, Or minimum selling price = 5.4(refer to Working Note ii) Working Note: I

85 Units Hours 5, 5, 1, 1, 1.8 = 8, hours 2, 2, = 12,8 hours Working Note: II 15, x 7,6, > 5, 15, x > 7,56, or x > 5.4 Alternative Solution: Total cost / unit of capacity 2, = 6.3 Weighted average selling price > 8.4 i.e. 5, , x > 6.3 2, = 5,, + 15, x > 6.3 2, = 15, x > 12,6, 5,, Or Ans. 59: Units 15, x > 7,6, x > 47.6 Minimum price to cover production Cost = 47.6 Minimum price to cover same amount of profit = 5.4 (refer to W orking Note 1) Working Note 1 ( ) 15, units = Rs. 5, 1 2, 2 1,6 4 1,28 8 1,24 Average/ hrs/u. Material Cost / u = 1, Variable cost = 2, Variable Cost = 12, Option I If both the orders came together, learning rate 8% applies and 8 units can be made, with average time of 1,24 hours per unit. Cost to PQ: Variable cost excl. labour = Rs.12, Labour cost 1,24 hrs 4 Rs./hr = Rs. 4,96

86 In this case, = Rs.16,96 Y Selling Price p. u. Rs.17,2 Rs.16,5 (under option I) Variable Cost p. u. Rs.16,96 X Rs.16,96 Contribution p. u. Rs.1,14 Rs.44 No. of units 4 4 Contribution (Rs.) Option II If X Ltd supplies its labour. 8% learning curve will apply to 4 units each of PQ & X. Hence: hrs/ u = 128 Y X Selling Price Rs.17,2 Rs.14, Variable Cost (excl. labour) Rs.12, Rs.12, Labour cost: Rs.5,12. Rs.128 Total Variable Cost Rs.17,12 Rs.13,28 Contribution Rs.8 Rs.72 Units 4 4 Contribution (Rs.) 32 2,88 3,2 PQ should not take labour from X Ltd. It should choose option I.