**MGKVP University Question Paper**** B.C.A. Examination, 2016**** Fourth Semester**

(Optimization Techniques)

Time :Three Hours Maximum Marks : 75

Note : Attempt any five questions. All questions carry equal marks.

Note : The answers to short questions should not exceed 200 words and the answers to long question

should not exceed 500 words.

**(a)**Old hens can be bought for Rs. 2.00 each but young ones cost Rs. 5.00 each. The old henslay

3 eggs per week and the young ones, 5 eggs per week, each being worth 30 paisa. A hen

costs Rs. 1.00 per week to feed. If I have only Rs. 80.00 to spend for hens, how many of each

kind should I by to give a profit of more than Rs. 6.00 per week, assuming that I cannot

house more than 20 hens?

Write a mathematical model of the above problem. You need not solve the problem. (7)**(b)**Solve graphically the following L.P.P. maximize. (8)

z = 3×1 + 2×2

Subject to the constraints :

-2×1 + x2 < 1 x1 < 2 xl + x2 < 3 x1, x2 > 0- Use Simplex method to solve the following L.P.P. : (15)

Maximize z = x1+ 2×2

Subject to : – x1+ 2×2 < 8, x1+ 2×2 < 12 x1- 2×2 < 3; x1 > 0 and x2 > 0 **(a)**Use Vogel’s Approximation method to obtain an initial basic feasible solution of the

transportation problem : (8)

Demand 200 225 275 250**(b)**Explain the difference between transportation problem and an assignment problem. Give a

mathematical formulation of the assignment problem. (7)- At a railway station, only one train is handled at a time. The railway yard is sufficient only for two

trains to wait while, the other is given the Signal to leave the station. Trains arrive at the station at

an average rate of 6 per hour and the railway station can handle them on an average of 12 per hour.

Assuming Poisson arrivals and exponential service distribution, find the steady-state probabilities

for the various number of trains in the system.

Also find the average waiting time of a new train corning into the yard. (15) - What is meant by replacement problem? Enumerate various types of solutions to the replacement

problem. Discuss in brief : group replacement and individual replacement policies. (15) - What are the motives for carrying inventory? Find the E.O.Q. problem with known shortages. (15)
- In a factory, there are Six jobs to perform, each of which should go through two machines A and

B, in the order A, B. The processing timing (in hours) for the jobs are given here. You are required

to determine the sequence for performing the jobs that Would minimize the total elapsed time, T.

What is the value of T.? 15

Job : J1 J2 J3 J4 J5 J6

Machine A 1 3 8 5 6 3

Machine B 5 6 3 2 2 10