BACHELOR'S DEGREE PROGRAMME

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Prudence Emerald Gaines
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1 No. of Printed Pages : 12 AOR-1 BACHELOR'S DEGREE PROGRAMME Term-End Examination CO June, 2012 (NJ CD (APPLICATION ORIENTED COURSE) AOR-1 : OPERATIONS RESEARCH Time : 2 hours Maximum Marks : 50 Note : Attempt 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 answers. (a) (b) (c) (d) (e) In an inventory model, the optimum order quantity decreases with the increase in shortage cost. In a project network, a non - critical activity cannot have zero total float. The dual of the dual is equivalent to the primal. The arrival rate in the Poisson distribution equals the mean of the exponential interarrival time. For a queueing model M/ M/ where the number of servers is infinite, the expected number of customers are determined by X/ where X and it denote the arrival and service rates, respectively. AOR-1 1 P.T.O.

2 2. (a) A toy company manufactures two - types 7 of dolls ; a basic version - Doll A, and a deluxe version Doll B. Each doll of type B takes twice as long to produce as compared to one of type A. The company would have time to make a maximum of 2000 per day if it produces the basic version only. The supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which these are only 600 per day available. The company makes a profit of Rs. 3 and 5 per doll, respectively, on Dolls A and B. Use the graphical method to find how many of each type of doll should be produced per day in order to maximise profit? (b) Find the shortest path from city A to city B 3 in the network map given below, using dynamic programming. 3. (a) The time taken (in hours) by four different 5 machines for completing 4 different jobs are given below. Find the optimal assignment and the optimal time taken to finish the jobs. AOR-1 2

3 Machine A BCD Jobs I II III IV (b) Find the sequence that minimises the total 5 time required to complete the following tasks on two machines : Task : I II III IV V VI Machine A: Machine B : Also find the total time taken when using this sequence. 4. (a) The jobs, predecessors of the jobs and 5 duration of the jobs, in a project are given below : Immediate Duration Jobs predecessor (in days), - 4 B - 6 C - 12 D A 6 E B 10 F C 8 G D 10 H F,E 7 I G, H 5 Draw the netwo, k diagram, and hence find the critical path and the optimal duration for completing the project. AOR-1 3 P.T.O.

4 (b) A bank plans to open a single server drive 5 in banking facility at a particular centre. It is estimated that 28 customers will arrive each hour on an average. If it requires 2 minutes to process a customer's transaction, determine the following (i) the proportion of time that the system will he idle ; (ii) how long the customer will have to wait before reaching the server. 5. (a) Consider the transportation problem having 5 the following cost and requirement table Destinations A B C Capacity (in units) Sources II III Demands (Units) Find an initial basic feasible solution using Vogel's method, and hence find the optimum transportation schedule. (13) The yearly demand for an item is 100 units, 5 ordering cost is Z 16 per order, and the inventory carrying cost is Z 0.5. The purchase price is Z 2 per item if the number of items purchased is less than 300 and it is Z 1 if the number of items purchased is 300 or more. Determine the optimum order quantity. AOR-1 4

5 6. (a) Three customs officers separately check the luggages of the passengers at an airport. The passengers arrive at an average rate of five per hour. The time a customs officer spends with a passenger is exponentially distributed, with mean service time 24 minutes. Find the probability that all the customs officers are idle. Also, find the probability that there are exactly 2 customers in the queue. (b) The final optimal table of some maximising LPP is.given below : 5 5 Pg Basic variables X 1 x 2 x 3 x 4 x 5 Solution 3 x /3 0 2/3 2 0 x /3 1 4/3 0 5 x A new constraint 2x1 + x2 is added to the original LPP. Find the changed optimal solution. 7. (a) Solve, by the simplex method, the following Linear Programming Problem : Max Z = 3x1 +5x2 +4x3 Subject to 2xi + 3X2 2x2 + 5x3 s 10 3x1 + 2x2 + 4x3 x1, x2, x3 0 AOR-1 5 P.T.O.

6 (b) A company manufactures 30 items per day. 4 The sale of items depends upon demand, which has the following distribution : Sales (Units) : Probability : The production cost and sale price of each unit are 40 and 50 respectively. Any unsold product is to be disposed of at a loss of 15 per unit. There is a penalty of 5 if the demand is not met. Use the following random numbers to estimate the total profit/loss for the company of the next 10 days. 10, 99, 65, 99, 95, 01, 79, 11, 16, 20 AOR-1 6

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8 2. (a) r) tr-d9-r f9trf-d-r lif--4-za 7 : TETtTRTT Iftzri A ict) 31cITE T1711 B. B -51-*T{ TIT:fT A 31-*-7 1,1 q9-r4 4)1 stil TriTzr c-nior t Trrqr-t-ur afqw-dir moo -a-f7ft ail c;cli tl -511-dkff 1500 lazir (A AT B t Loik-dch ch RT 61ci1 t I iloch 1-kzrr ct-1 -kft Fc-itq ttr 7ṟd-r-Tff tt ch) 1-N41 A 3 t B 1 9h 4-1k1: 3 T T. eci -g4tir -19-r.EFT FaRT 7114 fah IF* 31-N -watt t Fri YchR ch fwd 1-kza 3rF f9ftfu a,1 i~11 t (b) I ci -51) t1T tc4* Mt A # -141tB cich Er ff Pq : 3. (a) -c4r 3107 cht 3-1-FTT-31 d-tt 5 Tre--4 grr fffzrr TrITTI (..)if 4) rqii T ti fa--et-d ent4 T fff-zir,1,41 *tdc c1 AOR-1 8

9 A BCD 711 :f L II III IV (b) qt f41--iro1:gd chvit ch)qtr 5 q11~~ a,i rci zi,41) I H ill IV V VI 4-A7A : Trkti B : tri cta 3)ri ter, - 7r-A-R I 4c1 1M11 4. (a) -4),414.41,-ilf 414, ch 5, r-iche.d 44 31,-N 4., ad (k-ii -4) A. B 6 C - 12 D A 6 E B 10 F C 8 G D 10 H I F,E 7 I G, H 5 31-kla *77 c.r i-tft-q)wit ITE tit4 1 T-fr 72T 3fR wr-r 3TaftT 4-11cr s-tii I AOR-1 9 P.T.O.

10 (b) fl Via: t" T$-q--9 5 grati-r4r-o-4 t I 317AITF -07R{T,311clf t f-*7 ATM I grq T c #19-a 0,1a t F-11-16R5d ftql-r171 : (i) -5rurrl f9-nb-zt wpq 31-1-crru (ii) HO. 17fUT -ft-at r4711 i 5. (a) F (gcf 7P17 3fr 311cRqchc11 alfcichf 1 -ct 5 11f-{q-69 TITR;EIT C : T A B C 0-1(11 (..-*-1-4-t 14) I k.71c1 II III Tarr (F47-ēr) ito rarq Vtri 3-1-NR VTE ch itr cr`1z ft-d-f ā7 *te.c14-i 31Tth 4-117If i ri 1td ch-11 TR I (b) -q--q en) "qlfts4-4-{ Th fd 31Tg7 t, 347 4T ; 0.5 I qk 300 qtrf qvq1u-.1 -J 2 t. ath qk 300 TIT 31:1-# fr<-1 -q-rj1 c1141cf 7-41 TTT{T t I AOR-1 10

11 6. (a) -) 71{111 ch 3-TRTWI1 7{TW ffiT t I 11,1.13(rdElte 5 *1 311Tm T{ 141 ti 11 Irt ch ta 14 et-, Wr1:1 fa-zrr TRIT TriTzr * fir -4TRzi 24 firia *I TI111. W44 3-TrWiTzff Firtsh -0-F A7 I tlf- f 31-T-31-T T t T=14. I (b) 3T5TWalTh*-7131 LPP ch1 affait TZraTI TRIO 5 PB X1 x2 x3 x4 x5 (.4 3 X /3 0 2/3 2 0 x 4 0 2/3 1 4/3 0 5 x LPP 14 Li 91T 1-qtg 2x1 +x2 8,T115E I Alc11 t I t4rcircid te.c14 7. (a) ro rt.ld 13)13717 TITRzIT t-ch ql FaRT 6 Wrf-A-R : z=3x1 +5x2 +4x3 r 3.11%.1-* d1:11m-tut WrE4R, +3x2 2x2 +5x3 3xi +2x2 +4x3 15 x1, x2, x3 > 0 AOR-1 11 P.T.O.

12 (b) 1=Ert -51fdf t.1,1 4 1:17fiii-{Tert1 fw:f*1 cid-1 4 I Fri cr t : (chiq't): : rwicf 3-thfq-A- Ik9114-Ri: 40 T T. t I ft# `ift atifqk 15T. 11-cl 7*-r1 1:R c -cf fq-zrr t 144f q ifrrr yidel Ti-k Fri 5 T. sti 31Tr 10 rq-11' t rc-r ii5r,c9q) 4&sgraiI tr -9-trr 10, 99, 65, 99, 95, 01, 79, 11, 16, 20 AOR-1 12

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

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