## OPERATIONS RESEARCH Previous Question Papers JNTU

Time: 3 hours Max. Marks.80

Answer any Five questions

All questions carry equal marks

1. A farmer has a 100 acre –farm. He can sell all the tomatoes, lettuce , radishes he can raise. The

price he can obtain is Re 1 per kg for tomatoes, Re 0.75 a head for lettuce and Rs 2 per kg for

radishes. The average yield per acre is 2000 kg of tomatoes, 3000 heads of lettuce and 1000 kg of

radishes. Fertilizer is available at Re 0.5 per kg and the amount required per acre is 100 kg each

for tomatoes and lettuce and 50 kg for radishes. Labour required for sowing, cultivating and

harvesting per acre is 5 man-days for tomatoes and radishes and 6 man-days for lettuce. A total of

400 man-days of labour are available at Rs 20 pe man day. Solve the LPP in order to maximize

the farmer’s total profit. [16]

2. Solve the following transportation problem

GODOWNS

1 2 3 4 5 6 Stock

Available

7 5 7 7 5 3 60

9 11 6 11 - 5 20

11 10 6 2 2 8 90

1

Factory 2

3

4 9 10 9 6 9 12 50

Demand 60 20 40 20 40 40

It is not possible to transport any quantity from factory 2 to godown 5. Is the solution unique? If

not give alternate solution. [16]

3.a. Determine the optimal sequence for the problem given below which minimizes the total elapsed

time. Machining order is BA. The times given are in hours

Jobs 1 2 3 4 5 6 7

Machine A 3 12 15 6 10 11 9

Machine B 8 10 10 6 12 1 3

b. Solve the traveling salesman problem given by the following data

C12 = 20, C13 = 4, C14 = 10, C23 = 5, C34 = 6, C25 = 10, C35 = 6, C45 = 20

where Cij = Cji and there is no route between cities i & j if the value for Cij is not shown. [16]

4. A manufacturer is offered two machines A and B. A is priced at Rs 8000 and maintenance costs

are estimated at Rs 500 for the first year and an equal increment of Rs 100 from second to fifth

year and Rs 1500 for the sixth year and an equal increment of Rs 500 from seventh year onwards.

Machine B which has the same capacity is priced at Rs 6000. The maintenance costs of machine B

are estimated at Rs 1000 for the first year and an equal yearly increment of Rs 200 thereafter. If

money is worth 15% per year, which machine should be purchased? Assume that the scrap value

of each of the machines is negligible at any year.

5.a. Explain:

i) Pure and mixed strategy

ii) Maximin and Minimax criteria

iii) Saddle Point.

b. Solve the following game using principle of dominance

Player B

B1 B2 B3 B4 B5 B6

A1 4 2 0 2 1 1

A2 4 3 1 3 2 2

Player A A3 4 3 7 -5 1 2

A4 4 3 4 -1 2 2

A5 4 3 3 -2 2 2

6. A super market has two sales girls at the sales counters. If the service time for each customer is

exponential with a mean of 4 minutes, and if the people arrive in a poisson fashion at the rate of

10 an hour, calculate

i. Probability that there is no customer in the system.

ii. Average number of customers in the queue

iii. Average number of customers in the system.

iv. Average waiting time in the queue

v. Utilization factor. [16]

7.a. Explain various costs associated with inventory.

b. A manufacturer requires 15000 units of a part for an assembly operation. The company can

produce this part at the rate of 100 units per day. The set up cost for each production run is Rs 50.

To hold one unit of this part in inventory costs Rs 5 per year. Shortage cost is Rs 15 per unit per

year. Cost of the part is Rs 20 per unit. Assuming 250 working days per year find:

i) Optimum manufacturing quantity

ii) time between two production runs

iii) total cost of the inventory system. [8+8]

8. A student has to an examination in four courses P, Q, R and S. He has seven days available for

study. He feels that it would be better to devote a whole day to study one course so that he may

study a course for one day, two days, three days and so on or not at all. His estimates of marks he

may get according to days of study he puts in are as follows:

Course

P Q R S

0 0 0 0 0

1 2 3 2 1

Study days 2 4 5 3 3

3 6 7 4 5

4 7 9 5 6

5 8 10 5 7

6 9 11 5 8

7 9 12 5 8

Using dynamic programming find the number of days to be allocated to each course in order to

maximize the marks?