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Posted By: kishore Member Level: Gold Posted Date: 18 May 2008
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2007 Jawaharlal Nehru Technological University M.C.A Computer Aplications OPERATIONS RESEARCH Question paper
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1. A company produces two types of leather belts, say type A and B. Belt A is of a superior quality and Belt B is of a lower quality. Profits of two types of Belts are 40 and 30 paise per belt respectively. Each belt of type A requires twise as much time as required by a belt of type B. If all the belts were of type B the company would produce 1000 belts per day. But the supply of leather is sufficient for 800 per/day. Belt A requires a fancy buckles and 400 fancy buckles are available for this per day. For belt of type B only 700 buckles are available per day. How should the company manufacture the two types of belt in order to have maximum overall profit.
2. Minimize z = x1 – 3x2 + 2x3
Subject to
3x1 - x2 + 3x3 = 7
-2x1 + 4x2 = 12
-4x1 + 3x2 + 8x3 = 10
and x1, x2 ,x3 = 0
3. Find the optimal solution to the following transportation problem
Destination
5
4
8
6
5
600
4
5
4
3
2
400
3
6
5
8
4
1000
Ware house
450
400
200
250
300
OR
4. A company is faced with the problem of assigning 4 machines to 6 different jobs (one machine to one job only). the profits are estimated as follows:
Machine
A
B
C
D
1
3
6
2
6
2
7
1
1
4
3
3
8
5
8
4
6
4
3
7
5
5
2
4
3
Job
6
5
7
6
4
Solve the problem to maximize profit
Contd….2
Code No: OR-35/MCA -2-
5.a) Explain two person zero sum games.
b) Two competitors A and B are competing for the same product. Their different strategies are given in the following payoff matrix. Solve the game.
Pay off matrix for company A
Company B
I
II
III
IV
I
3
2
4
0
II
3
4
2
4
III
4
2
4
0
Company A
IV
0
4
0
8
6. Assume that present value of one rupee to be spent in a year time is Rs. 0.90 and C = Rs 3000, capital of equipment and the running costs are given in the table below:
Year
1
2
3
4
5
6
7
Running costs Rs.
500
600
800
1000
1300
1600
2000
When should the machine be replaced.
7.a) Customers arrive at a box office window, being manned by a single individual, according to a poisson input process with a mean rate of 20 per hour. The time required to serve a customer has an exponential distribution with a mean of 90 seconds. Find the average waiting time of a customer.
b) An item is produced at the rate of 50 items per day. The demand occurs at the rate of 25 items per day. If the setup cost is Rs. 100 per run and inventory cost is Rs. 0.01 per unit of item per day find the economic lot size for one run. Assuming that shortages are not permitted.
8.a) Find the sequence that minimizes the total time required in performing the following jobs on three machines in the order ABC job
Job
1
2
3
4
5
6
A
8
3
7
2
5
1
B
3
4
5
2
1
6
C
8
7
6
9
10
9 b) Minimize Z = 2 2 2
1 2 3 y +y +y
Subject to y1 y2 y3 = 27
y1, y2, y3 = 0
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