Operations Research MCC Prelims Question Paper 2013

Operations Research

Only use of basic calculator is allowed

Graph paper will be provided if needed

Section I is compulsory and solve any three from Section  II

Section I

Q.1) answer the following question briefly                                                                                                (15)

a)       What are the limitations of linear programming?

b)      What is mean by shadow price of resource?

c)       How do you resolve degeneracy is an assignment problem?

d)      What is mean by float? Explain free and interfering float?

e)      What is decision between decision making under risk and decision making under uncertainty?

Q.2) a company produces two products A and B wit h the help of three machines M1, M2 and M3.profit per unit is Rs.3 for A and Rs.5 for B. capacities for machines is 4,6,12 hrs. Respectively.

Following simplex solution is obtained. Based on this solution answer the solutions given below

X1 and X2 represent product A and B.S2 and S3 are slack variables for machines M1, M2 and M3 used for production. Capacities of machines are 4,6,12 hrs. respectively

Question:-

1. Is this optimal solution?                                                                                                                  (2)
2. Is this unique solution?                                                                                                                   (2)
3. Is the solution infeasible?                                                                                                                (1)
4. Is there degeneracy in the solution?                                                                                             (2)
5. What is the product mix and the maximum profit?                                                                    (2)
6. Which resources are scarce and which are abundant?                                                               (2)
7. If one unit of product becomes unavailable what is the reduction in maximum profit?       (2)
8. If due to maintenance, M3 is shut down for 2hrs, what will be effect on profit?                   (2)

Section II

M/S MCC sells two products A and B.the contribution of A and B is Rs.30 and Rs. 30 respectively. The production process has capacity of 30, 000-man hrs. it takes three man hours to produce a unit of A and 1 man hour to produce a product of B.maximum 8,000 units of A and 12,000 units of B can be sold. Formulate this as a linear programming to maximize contribution and solve by simplex method                                   (10 marks)

a)      Check whether the solution is optimal ?                                                                                                 (5)

b)      Is there any alternate solution present ?                                                                                                (3)

c)       If the warehouse offers to reduce his rate to route C to R, by how much the rate should be reduced such that warehouse C will get business                                                                                (2)

Q.5) following are the seven activities involved in the completion of small project

Determine optional time and additional cost for project completion.                                                        (10)

Q.6) a)  consumer good company has to decide which model of ne w brand of sports should keep. Projected profit for each model of the new brand for each possibility is given below.

Identify which product the company should stock using HURWIEZ alpha (a=0.7) and Laplace criteria    (6)

b) a water purification product manufacturer wants to set up a plant in western region . The demand can be either normal or high with probabilities 0.6 and 0.4 resp. normal demand is 50000 units and high demand is 80000 units. Cost of setting up plant is Rs.35 lakhs for normal capacity and Rs.50 lakhs for large capacity. After setting up a normal capacity plant. if company wants to go for a company extension additional cost will be Rs.20 lakhs. Profit under normal demand would be Rs.60 lakhs and under high demand Rs.90 lakhs. Construct a decision tree and identify the best alternative.                                       (4)