Group B

Attempt any SIX questions.

2. Describe briefly the tools and techniques of Operations Research.

3. Explain the ABC inventory planning system. An auto industry purchases spark plugs at the rate of Rs. 25 per piece. The annual consumption of spark plugs is 18,000 units. If the ordering cost is Rs. 250 per order and the carrying cost is 25% per annum, what would be the EOQ? If the supplier of spark plugs offers a discount of _____ for an order quantity of 3,000 units per order, do you accept the discount offer?

4. Reduce the following two-person zero-sum game to a 2 × 2 order by the dominance rule and obtain the optimal strategies for each player and the value of the game.

Player A	Player B
Player A	B₁	B₂	B₃	B₄
A₁	3	2	4	0
A₂	3	4	2	4
A₃	4	2	4	0
A₄	0	4	0	8

5. A radio mechanic, on average, finds 5 customers coming to his shop every hour for repairing their radio sets. He disposes of each customer within 10 minutes on average. The arrival and service times follow Poisson and exponential distributions, respectively. In light of the above facts, determine:

The proportion of time during which his shop remains empty.
The average number of customers in the system and in the queue.
The average time spent by a customer in the queue and in the system.
The probability of finding at least five customers in his shop.

6. Carew's machine shop has four machines on which three jobs have to be done. Each job can be assigned to one and only one machine. The cost (in Rs.) of assigning each job to each machine is given below.

Job	Machines
Job	P	Q	R	S
A	45	60	70	80
B	20	32	42	47
C	25	37	47	55

Req: What are the job assignments that will minimize the total cost?

7. Write the meaning of duality. What are the major steps in formulating dual linear programming problems? Justify with an example.

8. Write short notes on (Any Two):

Meaning of Degeneracy in Transportation Problem
Queueing Theory
Assignment Problem Algorithm

Group C

Attempt any TWO questions.

9. What is Game Theory? State the assumptions underlying it. Discuss its importance in business decisions.

10. Maximize

Subject to the constraints:

11. Jack Evan owns several trucks used to haul crushed stone to road projects in the country. The road contractor for whom Jack hauls, N. Teer, has given Jack the following schedule for next week:

Project	Requirement per Week	Plant	Available per Week
A	50	W	45
B	75	X	60
C	50	Y	60

Jack estimates his transportation cost from each crushing plant to each road project as follows:

From	To
From	A	B	C
W	4	8	3
X	6	7	9
Y	8	2	5

Req: Compute Jack's optimal hauling schedule for the next week and his transportation cost.

Operations Research 2024-2 Board Exam Question

Operations Research 2024-2 Board Exam Question