Question Paper: Operations Research Question Paper - Dec 17 - Computer Science (Semester 6) - Visveswaraya Technological University (VTU)
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Operations Research - Dec 17

Computer Science (Semester 6)

Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1(a) Define OR. Explain the nature and impact of OR. (10 marks)

1(b) Old hens can be bought at Rs. 2 each but young ones at Rs. 5 each. The old hens lay 3 eggs per week and the young ones lay 5 eggs per week, each egg being worth 30 paise. A hen (young/old) cost Rs. 1 per week to feed. You have only Rs. 80 to spend for buying hens. How many of each kind should you buy to give a profit of more than Rs. 6 per week, assuming that you cannot house more than 20 hens. Write a mathematical model of the problem. (10 marks)

2(a) Explain the concept of ice breaking in simplex method. (10 marks)

2(b) Use simplex method to solve the following LPP:
Maximize Z = 4x1 + 10x2
Subject to constraints: 2x1 + x2 ≤ 50
2x1 + 5x2 ≤ 100
2x1 + 3x2 ≤ 90
and x1, x2 ≥ 0
(10 marks)

3(a) Explain the post optimality analysis in simplex method. (10 marks)

3(b) Solve the following LPP by using Big M Method.
Maximize Z = 6x1 + 4x2
Subject to constraints: 2x1 + 3x2 ≤ 30
3x1 + 2x2 ≤ 24
x1 + x2 ≥ 3
and x1, x2 ≥ 0
(10 marks)

4(a) Explain the economic interpretation of duality with an example. (10 marks)

4(b) Solve the following LPP by using revises simplex method.
Maximize Z = x1 + 2x2
Subject to constraints: x1 + x2 ≤ 3
x1 + 2x2 ≤ 5
3x1 + x2 ≤ 6
and x1, x2 ≥ 0
(10 marks)

PART-B
5(a) Explain the essence of sensitivity analysis. (05 marks)

5(b) Solve the following LPP by using dual simplex methd.
Maximize Z = 2x1 + x2
Subject to constraints
x1 + 2x2 ≤ 10
x1 + x2 ≤ 6
x1 - x2 ≤ 2
x1 - 2x2 ≤ 1
and x1, x2 ≥ 0
(15 marks)

6(a) Explain Hungarian Algorithm to solve assignment problem. (10 marks)

6(b) Solve the following Transportation problem.
i) Use minimum cost method for IBFS
ii) Use u-v method for obtaining optimum solution

Supply points
4 6 8 8 40
6 8 6 7 60
5 7 6 7 50
Demand points 20 30 50 50

(10 marks)

7(a) Explain the following terms:
i) Pure stratergy
ii) Mixed stratergy
iii) Saddle point
iv) Payoff matrix
v) Two-person zero sum game.
(10 marks)

7(b) Obtain the optimum stratergies for both persons and the value of the game for zero-sum wo-person game whose payoff matrix is as follows:
 1 -3
 3  5
-1  6
 4  1
 2  2
-5  0
(10 marks)

8 Write a short notes on:
a. Nature of Metaheuristic
b. Tabu Search algorithm
c. Genetic algorithm
d. Simulated Annealing.
(20 marks)

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