## OPERATIONS RESEARCH JNTU previous years question papers

Time: 3 hours Max. Marks.80

Answer any Five questions

All questions carry equal marks

1. Solve the following problem by Big M method

Maximize Z = x1 + 2x2 +3x3 – x4

Subject to x1 + 2x2 +3x3 = 15

2x1 + x2 +5x3 = 20

x1 + 2x2 +x3 + x4 = 10

x1, x2, x3, x4 = 0. [16]

2. A product is produced by four factories A,B,C and D. The unit production costs in them are Rs 2,

Rs 3, Re 1 and Rs 5 respectively. Their production capacities are, factory A – 50 units, B – 70

units, C – 30 units and D – 50 units. These factories supply the product to four stores, demands of

which are 25, 35,105 and 20 units respectively. Unit transport cost in rupees from each factory to

each store is given in the table below

Stores

1 2 3 4

A 2 4 6 11

B 10 8 7 5

C 13 3 9 12

Factories

D 4 6 8 3

Determine the extent of deliveries from each of the factories to each of the stores so that the total

production and transportation cost is minimum. [16]

3.a. Solve the following traveling salesman problem

Cities 1 2 3 4 5

1 -- 16 18 13 20

2 21 -- 16 27 14

3 12 14 -- 15 21

4 11 18 19 -- 21

5 16 14 17 12 --

b. Four operators O1, O2, O3 and O4 are available to a manager who has to get 4 jobs J1, J2, J3, and J4

done by assigning one job to each operator. The time needed by different operators for different

jobs is given in the matrix below. How should the manager assign jobs so that the total time needed

for all four jobs is minimum? [16]

J1 J2 J3 J4

O1 12 10 10 8

O2 14 12 15 11

O3 6 10 16 4

O4 8 10 9 7

4. A company is planning to replace an equipment whose purchase cost is Rs 1, 00,000. The

operating and maintenance cost of the equipment during its first year of operation is Rs 10000 and

it increases by Rs 2000 every year thereafter. The resale value of the equipment at the end of the

first year of its operation is Rs 65000 and it decreases by Rs 10,000 every year there after. When

should the equipment be replaced if:

i. time value of money is ignored

ii. if discount rate is 12%.

5.a. Explain principle of dominance with an example.

b. Solve the following game graphically. [8+8]

Player B

I II III IV V

Player A I 4 2 5 -6 6

II 7 -9 7 4 8

6a. Explain the characteristics of a queuing system.

b. A repairman is to be hired to repair machines which breakdown at an average rate of 3 per hour.

The breakdowns follow poisson distribution. Non-productive time of a machine is considered to

cost Rs 10 per hour. Two repairmen have been interviewed – one is slow but cheap, while the

other is fast but expensive. The slow repairman charges Rs 5 per hour and repairs machines at the

rate of 4 per hour. The fast repairman charges Rs 7 per hour and he repairs machines at an average

rate of 6 per hour. Which repairman should be hired? [8+8]

7. An electronic equipment contains 500 resistors. When any resistor fails, it is replaced. The cost of

replacing a resistor individually is Rs 20. If all the resistors are replaced at the same time, the cost

per resistor is Rs 5 . The percentage surviving S(i) at the end of month i is given in the table

Month i 0 1 2 3 4 5

S ( i) 100 90 75 55 30 0

What is the optimum replacement plan? [16]

8.a. Explain the characteristics and applications of dynamic programming.

b. Write short notes on simulation languages