SECTION - A

1. What is the significance of operations research? What are the limitations of OR?

2. What are the basic concepts of linear programming?

3. Solve the following LPP using graphical method

Minimize Z = 20X₁ + 10X₂

Subject to, X₁ + 2X₂<40

                    3X₁ + X₂< 30

                    4X₁ + 3X₂>60

                       X₁, X₂ > 0

4. Use simplex method to solve the following LP problem

Maximize Z = X₁ + 3 X₂

Subject to 4X₁ + 2 X₂ < 40

                   3X₁ + 5X₂ < 60

                   10X₁ + 9X₂ < 90

                        X₁, X₂ > 0

5. Write short notes on:

a) Branch and bound method

b) Mixed IPP

c) Quadratic programming

SECTION - B

1. Explain the steps involved in solving a transportation problem.

2. Five men A, B, C, D, and E are available to do five jobs I, II, III, IV and V. The time that each man takes to do each job is given in the following matrix. Find the optimal assignment.

3. Explain the elements of a queuing system.

4. At a gas station one car arrives every 7.5 minutes. It takes 6 minutes for every car to get service. Arrivals are Poisson distributed and Services are exponentially distributed. Calculate

a) Utilization factor

b) Average number of cars waiting for service

c) Average time a car must wait for service

d) Average time a car has to spend at the gas station

5. Write short notes on

a) Transshipment model

b) Johnson’s rule for job sequencing

SECTION - C

1. a) Briefly describe Monte Carlo method of simulation

b) Differentiate between PERT and CPM

2. From the following matrix , the elements of which indicate the costs, obtain the decision using different principles of decision making:

3. A company manufactures around 150 mopeds. The daily production varies from 146 to 154 depending upon the variability of raw materials and other working conditions.

The finished mopeds are transported in a specially arranged lorry accommodating only 150 mopeds. Using following random numbers 80,81,76,75,64,43,18,26,10,12,65,68,69,61,57 simulate the process to find out

a) What will be the average number of mopeds waiting in the factory?

b) What will be the average number of empty spaces on the lorry?

4. A small project consists of seven activities whose time estimates are given in the following table.

a) Draw the network diagram

b) Identify the critical path and critical path duration

c) Calculate earliest start time, earliest finish time latest start time, latest finish time and float for each of the activities.

5. Write notes on

a) Elements of a decision model

b) Project crashing

CASE STUDY - 1

A firm is planning to develop and market a new drug. The cost of extensive research to develop the drug has been estimated at Rs 1,00,000. The manager of the research programme has found that there is a 60% chance that the drug will be developed successfully. The market protentail has been assessed as follows:

The present value figures do not include the cost of research. While the firm is considering this proposal, a second proposal, almost similar, comes up for consideration. The second one also requires an investment of Rs 1,00,000 but the present value of all profits is Rs 12,000. Of course the return on investment in the second proposal is certain.

a) Draw a decision tree indicating all the events and choices of the firm.

b) What decision the firm should take regarding the investment of Rs 1,00,000?

CASE STUDY - 2

A company has four factories manufacturing the same commodity, which are required to be transported to meet the demands of four warehouses. The supplies and demands as also the cost per transportation from factory to warehouse in rupees per unit of product are given below:

a) Derive and optimal strategy of transportation of goods from factories to warehouses and assess the optimal cost.

b) If a new transporter agrees to transport goods from factory C to warehouse W at a unit cost of Rs 50, analyze the impact of this on the current optimal solution.