Group B

Attempt any SIX questions.

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

3. A company combines Factor 1 and Factor 2 to form a product that weighs 100 kg. At least 50 kg of Factor 1 and no more than 60 kg of Factor 2 should be used. Factor 1 costs Rs. 25 per kilogram and Factor 2 costs Rs. 10 per kilogram. Use the Simplex Method to find the amounts of Factor 1 and Factor 2 that should be used to minimize the cost.

4. Write the Hungarian algorithm to solve the assignment problem.

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

From	To				Plant Capacity
From	A	B	C	D	Plant Capacity
W	3	2	7	6	5000
X	7	5	2	3	6000
Y	2	5	4	5	2500
Requirement	6000	4000	2000	1500

6. Discuss the queueing process with a suitable example of a queueing model. State its assumptions.

7. Write short notes on (Any Two):

Kendall's Notation
Types of Inventory System
Importance and Advantages of the Duality Problem

8. Food manufacturers Company 1 and Company 2 are competing for an increased market share. The payoff matrix shown below describes the increase in market share for Company 1 and the decrease in market share for Company 2. Determine the optimal strategies for both companies and the value of the game.

Company 1	Company 2
Company 1	Give Coupons	Decrease Price	Maintain Present Strategy	Increase Advertising
Give Coupons	2	-2	4	1
Decrease Price	6	1	12	3
Maintain Present Strategy	-3	2	0	6
Increase Advertising	2	-3	7	1

Group C

Attempt any TWO questions.

9. Solve the duality problem.

Minimize the cost:

Subject to:

10. There are four workers assigned to four tasks. The workers have different efficiencies, and the tasks have different difficulty levels. The estimated profit (in rupees) for each worker is given below. How should the tasks be allocated to maximize the total earnings?

Workers	Tasks
Workers	Task 1	Task 2	Task 3	Task 4
A	5	40	20	5
B	25	35	30	25
C	15	25	20	10
D	15	5	30	15

11.

a) Find the cost per period of the individual replacement policy for an installation of 3000 light bulbs, given the following:

Cost of replacing an individual bulb is Rs. 20.
The cumulative probability of failure is given below.

Months	0	1	2	3	4
Cumulative Probability of Failure	0	0.1	0.3	0.8	1.0

Calculate the number of light bulbs that would fail during each of the four months.

b) Write the algorithm for solving the transportation problem and obtaining the optimal solution using the MODI Method.

Operations Research 2025 Board Exam Question

Operations Research 2025 Board Exam Question