Attempt all the problems.

Section-A

problem1) prepare brief note to describe the following:

a) Use of Sensitivity Analysis in Linear Programming. Particularly highlight the use of “Shadow Prices” and “Reduced Cost”.

b) Use of Goal Programming. How it differs from Linear Programming?

problem2) Use Simplex method to solve the following L.P. problem.

Maximize : Z =  2X1 – X2 + X3

Subject to the constraint:

3X1 + X2 + X3   ≤  60
X1 - X2 + 2X3   ≤  10
X1 + X2 - X3   ≤    20
X1, X2, X3 ≥   0

problem3) prepare brief note on the following:

a) Zero – Sum Game

b) Pure and Mixed Strategies in Game theory

c) Using Utility concept to arrive at decisions

d) Assumptions that are made for switching problems in Markov Chain.

problem4) Describe the following in a Transportation Problem.

a) How to determine that there are multiple solution

b) What meant is degeneracy. What does it signify about nature of constraints.

c) What are the methods by which Initial Feasible solution could be obtained.

Section-B

A firm has developed the new storage device for computers and should now decide what do with the idea. The expected life of the product is 10 years. One possibilities to immediately least the products rights to a different company which would market and sell the product. The form expects to gain Rs. 2.25Cr as fees. Two other possibilities exists. These are to build the large manufacturing plant now to product the product or build a small plant now to produce with option to expand plant in 4 years. The expected payoff from producing the product depends on the market acceptance of the product in the first 4 years and during last 6 years. If the market acceptance of product in the first 4 years is low, the firm would stop production and reduce losses at this point. It is felt that there is a 70% chance of high market acceptance for product in the first 4 years. If the market acceptance is high in the first 4 years the probability of a high market acceptance in the next years is 60%. The following table given net payoff’s estimated in crores of Rupees for the product.

Market acceptance

First 4 years    Next 6 years    Large plant    Small plant Don’t expand    Small plant Expand

High                     High                 7.5                            5                               6
High                     Low                  2                              3                               2
low                        -                   (1)                            1.5                              -
You are needed to give your recommendation to the firm ?