## 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 = 4x_{1} + 10x_{2}

Subject to constraints: 2x_{1} + x_{2} ≤ 50

2x_{1} + 5x_{2} ≤ 100

2x_{1} + 3x_{2} ≤ 90

and x_{1}, x_{2} ≥ 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 = 6x_{1} + 4x_{2}

Subject to constraints: 2x_{1} + 3x_{2} ≤ 30

3x_{1} + 2x_{2} ≤ 24

x_{1} + x_{2} ≥ 3

and x_{1}, x_{2} ≥ 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 = x_{1} + 2x_{2}

Subject to constraints: x_{1} + x_{2} ≤ 3

x_{1} + 2x_{2} ≤ 5

3x_{1} + x_{2} ≤ 6

and x_{1}, x_{2} ≥ 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 = 2x_{1} + x_{2}

Subject to constraints

x_{1} + 2x_{2} ≤ 10

x_{1} + x_{2} ≤ 6

x_{1} - x_{2} ≤ 2

x_{1} - 2x_{2} ≤ 1

and x_{1}, x_{2} ≥ 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)