Group B

Attempt any SIX questions. [6×5=30]

2. What is Operational Research? Explain the general methods of solving OR models.

3. A chair manufacturing company produces two types of chairs, A and B, using three machines, X, Y, and Z. The time required for each chair on each machine and the maximum time available on each machine are given below:

Machine	Time Required for Each Type		Maximum Time Available (Hours per Week)
Machine	A	B	Maximum Time Available (Hours per Week)
X	6	8	120
Y	3	5	100
Z	12	4	144

The profit on chairs A and B is Rs. 500 and Rs. 300, respectively. What combination of chairs should be produced to obtain the maximum profit?

4. Write an algorithm to minimize the solution of LPP using the Simplex Method.

5. Given the following transportation framework, find the optimal solution.

From	To			Plant Capacity
From	A	B	C	Plant Capacity
X	1	2	1	160
Y	7	1	160	240
Z	2	160	35	35
Requirement	65	35	35	115

6. Find the cost per period of the machine replacement policy of an installation given in the following table. The 200 street lamps are considered. The cost of replacing an individual bulb is given in Table (b). The cumulative probability of failure is given below.

Week	0	1	2	3	4	5
Cumulative Probability of Failure	0	0.1	0.3	0.5	0.7	1.0

7. Discuss the single-channel queueing model with a suitable example. Give its assumptions.

8. Write short notes on (Any Two):
a) Kendall's Notation
b) Big M Method
c) Importance and Advantages of the Duality Problem

Group C

Attempt any TWO questions. [2×10=20]

9. Using duality, solve the following LPP:

Minimize:

z = 20x₁ + 40x₂

Subject to:

3x₁ + 6x₂ ≥ 600
5x₁ + 12x₂ ≥ 36
20x₁ + 10x₂ ≥ 100
x₁, x₂ ≥ 0

10. A City Corporation has decided to carry out maintenance work in the city. There are four tasks to be completed using five contractors. Which of these contractors should be assigned to those tasks? Solve the assignment problem to obtain the best result.

Contractor	Task 1	Task 2	Task 3	Task 4
A	19	24	37	28
B	18	37	28	39
C	19	28	31	26
D	30	16	28	30
E	20	25	31	26

11.
a) Two types of food manufacturers are competing for an increased market share. The payoff matrix describes the increase in the market share of A and the decrease in the market share of B. Determine the optimal strategies for both manufacturers and the value of the game.

A \ B	Strategy of B
A \ B	Give Price	Decrease Price	Maintain Present Strategy	Increase Advertising
Give Price	25	20	14	8
Decrease Price	27	16	12	14
Maintain Present Strategy	35	8	15	6
Increase Advertising	-2	8	13	5

b) Write the Hungarian algorithm to solve the assignment problem.

Operations Research 2023 Board Exam Question

Operations Research 2023 Board Exam Question