## OPERATIONS RESEARCH JNTU Previous Question Papers - jntuquestionpapers.com

Time: 3 hours Max. Marks.80

Answer any Five questions

All questions carry equal marks

1. Obtain the dual of the following primal problem and solve it.

Minimize z = x1 – 3 x2 – 2 x3

Subject to

3x1 – x2 + 2x3 = 7

2x1 – 4x2 = 12

- 4 x1 +3x2 + 8x3 = 10

x1, x2 = 0 , x3 is unrestricted [16]

2. Solve the following transportation problem. The elements in the matrix are the cost of

transportation in Rupees per unit transported. [16]

Warehouses

Factories A B C D E Availability

W 4 3 1 2 6 40

X 5 2 3 4 5 30

Y 3 5 6 3 2 20

Z 2 4 4 5 3 10

Requirement 30 30 15 20 5

3. A Company has four territories open and four salesmen available for assignment. The territories

are not equally rich in their sales potential; it is estimated that a typical salesman operating in each

territory would bring in the following annual sales:

Territory I II III IV

Annual Sales ( Rs) 60,000 50,000 40,000 30,000

The four salesmen are also considered to differ in ability; it is estimated that working under the

same conditions, their yearly sales would be proportionately as follows: [16]

Salesman A B C D

Proportion 7 5 5 4

Assign the salesmen to the territory if the criterion is maximum expected sales.

4. For M/M/1 : 8 /FCFS Derive an expression for:

(i) Average number of customers in the system

(ii) Probability of having n customers in the system

(iii) Average queue length

(iv) Average waiting time in the system [16]

5. An engineering company is offered two types of material handling equipment A and B. A is

priced at Rs 60,000/- including cost of installation, and the costs for operation and maintenance

are estimated to be Rs 10,000/- for each of the first five years, increasing by Rs 3,000/- per year in

the sixth and subsequent year. Equipment B with a rated capacity same as A, requires an initial

investment of Rs 30,000/- and operation and maintenance costs are estimated to be Rs 13,000/-

per year for the first six years, increasing by Rs 4,000/- per year for each year from 7th year

onwards. If money is worth 10% determine which equipment the company should buy. Neglect

the scrap value of the equipment.

6.a. Explain the Principle of dominance to reduce the size of the pay off matrix.

b. Solve the following game graphically. [16]

Player B

B1 B2

A1 1 -3

A2 3 5

Player A A3 -1 6

A4 4 1

A5 2 2

A6 -5 0

7. A manufacturing company purchases 9000 parts of a machine for its annual requirements,

ordering one month usage at a time. Each part costs Rs 20. The ordering cost per order is Rs 15

and the carrying charges are 15% of the average inventory per year. You have been assigned to

suggest a more economical purchasing policy for the company. What advice would you offer and

how much would it save the company per year. [16]

8. Customers arrive at a milk booth for the required service. Assume that inter-arrival and service

times are constant and given by 1.8 and 4 time units, respectively. Simulate the system by hand

computations for 20 time units. What is the average waiting time per customer? What is the

percentage idle time of the facility? Assume that the system starts at t=0.