**December, 2009**

**Ms-51 : Operations Research**

1. Solve the following problem through SIMPLEX method.

Minimize Z = — 3x_{1}+ x_{2}+ x_{3}

Subject to

x_{1} —2x_{2} + x_{3} < 11

—4x_{1}+ x_{2} + 2x_{3} > 3

— 2x_{1} + x_{3} = 1

x_{1} > 0, x_{2 }> 0 and x_{3} >0

2. (a) Discuss the queue parameters. How do you specify a querraing system ?

(b) A refuelling station is served by a single pump machine for providing service to the petrol vehicles. The arrival process has shown that the distribution of times between arrivals is negative exponential with a mean of 10 minutes. Similarly, service times were found to be adequately described by a negative exponential distribution with a mean of 6 minutes. Waiting space is unlimited. Determine:

(i) Probability that the customer has to wait.

(ii) Mean number of customer in the system.

(iii) Percentage utilisation of the service station.

(iv) Steady - state probability of having four customers in the system.

3. (a) Define Operations Research. Discuss its application in manufacturing and non - manufacturing sectors.

(b) State and explain Bellman's Principle of optimality.

4. (a) Write the general form of LP problem in matrix notation.

(b) The demand of an item is uniform at a rate of 25 units per month. The fixed cost is Rs. 30/- each time a production is made. The production cost is Rs. 2/- per item and rinventory carrying cost is 50 paisa per unit per month. If the shortage cost is Rs. 3/-per item per month, determine how often to make a production and of what size ?

5. Write short notes on any three of the following :

(a) GOAL Programming

(b) GOMORY'S cutting plane Algorithm

(c) Selective Inventory Control

(d) Pure and Mixed Strategy

(e) Sensitivity Analysis

(f)