BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination June, 2013

Transcription

1 No. of Printed Pages : 15 AOR-01 O BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination June, 2013 (APPLICATION ORIENTED COURSE) AOR-01 : OPERATIONS RESEARCH Time : 2 hours Maximum Marks : 50 Weigh tage : 70% Note : Attempt any five questions in all. Question No.1 is compulsory. Do any four questions out of Question no. 2 to 7. Calculators are not allowed. 1. Which of the following statements are true and 10 which are false? Give reasons for your answer. (a) The assignment problem can be solved using simplex method. (b) The optimal values of the objective functions of the primal and dual problems are not same. (c) For each cell (i, j) in an optimal solution to a transportation problem the value (ui + vi c f.) xii= O. (d) For a queuing model (M/M/1):(GD/ co / co), if the service rate i. increases, the expected number of customers in the system decreases. AOR-01 1 P.T.O.

2 (e) In the inventory model with finite replenishment rate, if the replenishment rate is equal to consumption rate, the holding cost is (a) Solve the following LPP using graphical 6 method. Maximize 5x1 + 4x2 Subject to 6x1 + 4x x 1 + 2x 2- <6 x2 2 x 1 + x 2- <1 X1, X2?:- 0 (b) A leading firm has three auditors. Each 4 auditor can work up to 160 hours during the next month, during which three projects must be completed. Project I will take 180 hours to complete, Project II will take 140 hours and Project III will take 160 hours to complete. The amount per hour that is charged by cash auditor for each project is given below : Project I II III A Auditor B C AOR-01 2

3 Find an initial basic feasible solution to the problem using vogel's method. Also, find the cost. 3. (a) Write the canonical form of the following LPP. Minimize 5x1-7 6x2 4x3 Subject to 4x2 +6x x2 +2x x1 + 5x2 3x3 = 3 0, x3 unrestricted in sign. Also, write the dual. (b) Solve the following profit maximization 6 assignment problem. Job A Machine B C D AOR-01 3 P.T.O.

4 4. (a) A project schedule has the following 6 characteristics : Activity Time Activity Time (i) (ii) Construct the network diagram. Compute earliest and latest occurence times for each event. (b) Find the sequence that minimises the total time required to complete the following tasks on two machines : Task I H III IV V VI Machine A Machine B Find the total time taken when using this sequence. Also, find the idle time for each machine. AOR-01 4

5 5. (a) A large service station has a store room from 5 where the service mechanics take the parts for the jobs they work upon. The mechanics wait in the line to get the parts that they need. The store is manned by one attendant who can, on an average, attend 7 mechanics per hour, it is observed that, average arrival rate of the mechanics at the store is 5 per hour. Assuming that the pattern of mechanic's arrivals is Poisson distributed and the service time is exponentially distributed, determine. (i) (ii) (iii) (iv) the expected number of mechanics in the system. the expected number of mechanics waiting in the queue. the expected time that a mechanic has to spend in the queue. the expected time that a mechanic spends in the system. (b) The production department for a company 5 requires 7200kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is 72 and the cost of carrying inventory is 25 percent of the investment in the inventories. The price of raw material is 20 per kg. Find the economic order quantity (EOQ), the total cost per unit time and the cycle time. AOR-01 5 P.T.O.

6 6. (a) Use the dual simplex method to solve the 5 following LPP : Minimize z = 2x + 3y + z Subject to x + y + z 40 2x + y z 10 x, y, z 0 (b) Find the sequence that minimizes the total 5 elapsed time required to complete the following task. Each job is processed in the order ABC. Job : Machine A: Machine B: Machine C: Find the total elapsed time also. What would happen if the job are processed in the order BCA? 7. (a) Find the shortest path from city A to City B 5 in the network map given below : AOR-01 6

7 (b) A confectioner sells confectionary items. 5 Past data of demand per week with frequency is given below : Demand/week : Frequency : Use the following sequence of random numbers, simulate the random numbers for the next 10 weeks. 35, 52, 90, 13, 23, 73, 34, 57, 35, 83 AOR-01 7 P.T.O.

8 zcrrfa on ITftaTT ttft m-..- ch LlIckqc111-1 ) : fad FTFT : 2 3.7filThTiT 34- : 50 Tff 951 : 70% v?a. : To/ vita./q R: 1 sarriwteic i V.TT: 2 47 Trr - dth q7rutv chi Tcd7T (10 31TITM. 3g7t/ A 4) FR:rf A A 3.77FT k cbrui s3-r : (a) f971d7titrzrrvrn FIR! fachcli tl (b) 31g tt ITTRAT 3t4zi (c) -crrr TITITzIT *te.c14-1 chlrue.4)1 j) 1111 Vi cif) = 0 (d) f f9-q-qf (M/M/1):(GD/ co/ co), t Fri zifq Irzt71h1t w-iticfl IT74 4, 44 -er t A OR-01 9 P.T. O.

9 (e) -?ifq -1:-Tr4 dlia-tt t oltiqt 61c-1 t, ql.( '1) I 2. (a) Ixrch---1-zr faft -1 4-iFoRAcf LPP : 6 5x1 + 4x2 311T-* T-Tur : 6x1 +4x25_24 x 1 + 2x 2- <6 X2-2 x1 + < X 1, X 2 0 (b) a1h 'Atq--* Tr61-4 cn LiRi1A-ti3 rm, Q. cm 4-1 t Li 0 z1-11 I ch.) othit,,-04.)\1111ii140 3T1-{ I -17A-T i Fri tat- LR i;rfff 'Eft t fetr-4-4 TCRT t : I 1-1 II III A B C AOR-01 10

10 fq-n ixrtfirt 3-Tr4rt 7frrff -11cf --1f--A7I c1iid 711t fA7 I 3. (a) F-14--Trofuff LPP rci r d frif-g7 : 4 5x1-6x2 +4x3 chi 3-Tf4W-dift-Tur 3x1+4x2 + 6x3,?.- 9 xl +3x2 +2x3,5 2x1 + 5x2 3x3 =3 xi, x2?- 0, x3 3wra---4-RT-d t (b) f frtlard c1i4 3iNWT411M-77 f 4T cb 6 -grti \list A B C D AOR P.T.O.

11 4. (a) Q.chItils=1-11 &T T& 3T-Ffc-Ted u 1 6 "'fed-n. TM-4 ITI-d-f6ffq TI r (i) 3-1AT:1 I (ii) -5rTf7 TITP=1 airt 3f-d-14 Tr1T *-fo-ff (h) 1:17F 3-F & 4 rd 1,1 vr **4 q 1,1 r cfrkcit t : --r-4 : I II III IV V VI TIR-i17 A : B: w14 rt Tp=r-zr 711c-11-F7771 arc IT711-9" f c Trwzr 7-d-rt 7:f - 1.ft 711c1 ch-rr77 I AOR-01 12

12 5. (a) -) crt Trf F-1,4,31-Erkgm14)ki,311T-P4. *. rc-iki T4/ 1:1-1aT I 3-14kia. 1C-1111-kfi f' -wt9i..):c-fr wr4 ffir ff 7 4f-I ci-) -4-qr -1A-qrff cf.) tur -Frq-r 4 *T-d 5 to 14) 4F-ich.qt9 3T-14-r-{ 31T 4-{ rter 17 : c11.11) i 37-4rE-ff c-1,4 tr-14-1r-irt_lff TIM : (i) -Turrr il'ci-)fict-;1 1-)1 d err (ii) TE'ff Ti TcNIT (iii) chl -uffwr fw-d-8r 7-4-L1-7 d (iv) 51cgl qld -4-qzr 41d,F1 ah i)-u-rr- c-47.-ficl t I (b) '7W :t7l11q-i farm m1 fir fad 5 fai~~is~r IMF abi 7200 ft.;11. q3314rffc-virti c4h1h 72 * -4:11- qkul 0141d HIM trcl 11. fir 25% t 1 1:11 20 pfd iscb.t. *1 31If2iT' 3-14-{ 4-I Yid 7R-Trzr 0141c1 Ti-TP4 rs4 AOR P.T.O.

13 6. (a) fu-d- LPP fdfq 5 z =-- a +3y +z chi -Ticti-fichul WrrA71 : x+y+z?-40 2x+y-z?-10 x, y, z?- (b) gild ch 'ttl 5 -WT4 'k f' To:RI *1 7fq ch.1 ABC *4-114 f* : id: TRfi-9. A : :171ti B: :1(47 C : (1 zr 5-ft -T-1-fqu zirq BCAWIT14f*-zif \ARM 1411? 7. (a) ka-4 H11 cii WU A -q1ḡb chi 5 4cr AOR-01 14

14 (b) t I cirolltc-ittftd. -q-f-d. 5 7fit chi fcrorai-4--- r : Hin /77E-r- : otiqrctl : Ocl ilf-t;och -1tV-113fft 3-Tq-wIT -gm 3T-1-10 ti 4111 rm qi1r- 4,41 4&s.e.off chi 3-1T*717 35, 52, 90, 13, 23, 73, 34, 57, 35, 83 AOR-01 15