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USN 10ME74
Seventh Semester B.E. Degree Examination, Dec.2013 lJan.Zol4Operations Research
Time: 3 hrs. Max. Marks:100Note: Answer FIVEfull questions, selecting
qt least TWO questions from each part.
PART _ AI a. Old hens can be brought at Rs.50/- each and young hens can be brought at Rs.100/- each.
The old hens lay 3 eggs/week and young hen's 5/week. Each egg cost 2 Rs. A hen costRs.S/week to fbed, if a person has only Rs.2000 to spend for hens, formulate the problem todecide hoW many of each kind of hens should be buy? And he cannot house more than
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40 hens, formulate the problem a LPP model.b. Solve the following LPP by Graphical method,
Z,rror=3x, +4x,Subject to constraints,5x, + 4x, <200
3x,+5x, S1.50
5x, +4x, > 100
8x, +4x, > 80
2 a. Solve the following LPP using Simplex method:Zrrru*=10x,+5x,Subject to constrainls.4x,+5x, <100
5x,+2xr<80x, &x, >0
b. Solve the given problem by using Big.M.L,nir, = )xt +Jx2Subject to constraints,2x, + 4x, <12
2*, *2x, =lQ5x, +2xr>10x,&x, >0
3 a. Find the optimality tbr ble nd initial
(10 Marks)
(10 Marks)
(08 Marks)
(I2 Marks)
AM method. 1lo Marks)tven proDtem a mrt SO utron using V-------r.- OriginDestination]S---=--
W1 W, Wr Wa Supply
Fr 2 2 2 11J
Fz l0 8 5 4 7
F3 7 6 6 8 5
Demand 4 J 4 4
I of 3For More Question Papers Visit - www.pediawikiblog.com
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4 a. A traveling salesman has to visit 5 cities. He wishes to start from a particular city, visit each
3 b. A AML company has 5 tasks and 5 personsand to minimize the total cost.
10ME74
to perform. Determine the optimal assignment(10 Marks)
(10 Marks)
(14 Marks)(06 Marks)
(06 Marks)(07 Marks)
b. What is integer programming? Why it is needed and write the branch and bound algorithm.
PART _ B5a.Thefo1lowingtablegivestheuffiaconstructionprojectandotherrelated
city once and return to his starting ,"T nT the least cost route.
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Activity to t,, t1-2 20 30 461-3 9 t2 21
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4-5 t2 l8 24i) Draw a pert networkii) Calcutate project durationiii) Find the critical path.iv) Find the probability that the project will be completed within 50 days.
b. Define the following: i) Normal time ii) Crash time iii) Free float
6 a. Define: i) Fair game ii) Pure strategy iii) Mixed strategyb. Use dominance rule to trnd the optimum strategies for both the player.
Br B2 B3 Ba Bs 86A' F 2 o 2 t r-lorla 3 I 3 2 2
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Player A-, l4 3 7 -5 1 2ltu14 3 4 -r 2 z
IAsl_4 3 3 -2 2 2_lc. Solve the game by graphically method.
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JobsMachines
A B C D E
P 6 7 5 9 4
a 7 5 10 9 6
R 5 4 J 6 5
S 8aJ 5 6 4
T 4 7 5 6 6
(07 Marks)
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10ME74
a. Write the characteristics of waiting lines. (05 Marks)b. At what average rate must a clerk at super market work in order to ensure a probability of
0.9 that the customer will not have to wait longer than 12 minutes? It is assumed that there isonly one counter to which customer arrive in a Poisson fashion at an average rate of 15/hr.The length of service by the clerk has an exponential distribution. (07 Marks)
c. In a hair dress by saloon with one barber, the customer arrived follows Poisson distributionat an average rate of one every 45 minutes. The service time is exponentially distributedwith a mean of 30 minutes. Find:i) Average number of customer in a saloon.ii) Average waiting time of customer before service.iii) Average idle time of barber.
a. Define the following:D Idle time ii) Total elapsed time
b.
c.
(12 Marks)
.'l'
* {< * *.{e
(08 Marks)
(04 Marks)(04 Marks)Write the asSpmption underlying the sequencing problem.
Find the sequenCe that minimires the totalelaps ime and normal time.the tota EIADSEC time. idle t
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A B C D. EMI 6 8 7.. 10 6
Mz .,) 2 '.5 6 4
M3 4 8 6 7 8
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