Test Papers / Previous Question Papers of IGNOU MS51 Operations Research December 2005

MANAGEMENT PROGRAMME
Term-End Examination

June, 2005

MS51 : OPERATIONS RESEARCH

Time: 3 hours
Maximum Marks: 100
(Weightage 70%)

SECTION A

1. Discuss the historical background of Operations Research. Explain its significance and scope in Modern Management Enumerate the limitations of O.R. (20)

2. Using the graphical method, find the maximum value of
z = 7x₁ + 10x₂
subject to the constraints
x₁+x₂ ≤ 30000
x₂ ≤ 12000
x₁ ≥ 6000
x₁ ≥ x₂
x₁, x₂ ≥ 0 (20)

3. A company manufactures a product from its two plants P₁ and P₂ with a capacity of 200 units and 100 units per month. It supplies the product to four shops at S₁, S₂, S₃, and S₄ having a demand of 75, 100, 100 and 30 units respectively per month. The profit per unit differs with shops as given below in Rs.

4. Goodwill Manufacturing Company is currently purchasing 9000 units of a product for its annual usage. It is presently ordering one month usage at a time. Each unit costs Rs. 20. The ordering cost per order is Rs. 15 and carrying cost is 15% per annum. Find the optimal purchasing policy for the company. How much does the company save per year? (20)

5. (a) Discuss various steps of Goal programming model Formulation. How does GP help in decision making? (10)

(b) Give the characteristics of Integer programming. Explain the cutting plane method. (10)

SECTION B

6. In a bank where there is a single server, the arrival rate of customers is 5 per hour and service rate is 8 per hour, Assuming the conditions for the single channel queuing model, find out : (20)

(a) The probability that the serve is idle.
(b) The probability that there are at least two customers in the system.
(c) Expected time that a customer spends in queue.

7. (a) Find the saddle point in the following case and also the game value. (10)

        B
    4     2
A -2   -3
   -4   -5

(b) Discuss Simulation and its application in decision making. Explain Monte Carlo simulation giving examples. (10)