Tamil Nadu Open University (TNOU) 2009-2nd Year M.Sc Mathematics Tamilnadu open university Maths Operation research 2006 - 07 batch - Question Paper

M.Sc. DEGREE EXAMINATION
JUNE, 2009.

(AY 200607 batch onwards)

Second Year

Mathematics

OPERATIONS RESEARCH

Time : 3 hours Maximum marks : 75

SECTION A (5 5 = 25 marks)

Answer any FIVE of the following.

1.         Obtain the dual of the following linear programming problem

             Maximize

             subject to the constraints

             and .

2.         Explain the linear goal programming.

3.         Explain the concept of dynamic programming and the relation between linear programming and dynamic programming approach.

4.         Two players A and B match coins. If the coins match, then A wins two units of value, if the coins do not match, then B wins 2 units of value. Determine the optimum strategies for the players and the value of the game.

5.         If the two person, zero-sum game

             Player B

             Player A

             Strictly determinable and fair? Justify.

6.         Explain the queuing model.

7.         State the sufficient conditions in Lagranges multiple method.

8.         Show that the problem is separable.

SECTION B (5 10 = 50 marks)

Answer any FIVE of the following.

9.         Use simplex method to maximize

             subject to the constraints :

10.       Carry out three iterations of Karmarkars algorithm for the following problem :

             Maximize

             subject to

11.       Solve the network by cyclic algorithm

12.       Solve the following linear programming problem by dynamic programming

             Maximize

             subject to the constraints

13.       Use Branch and Bound method to solve the following their programming problem

             Maximize

             subject to

             and

14.       In a shop there is only one salesman at the counter. 9 customers arrive on an average every
5 minutes, while the salesman can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrivals and exponential distribution for service rate.
Find (a) average number of customers in the system,
(b) average number of customers in the
queue, (c) average time a customer spends in the system, and (d) average time a customer spends in the queue.

15.       Obtain the necessary conditions for the optimum solution of the following problem

             Minimize

             Subject to the constraint

             .

16.       Solve the following geometric programming problem

             Minimize .