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TAMIL NADU OPEN UNIVERSITY MCA - II (SEM 4) JUN 2010 : Operation Research

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MCA 766 MCA 16 M.C.A. DEGREE EXAMINATION JUNE, 2010. Second Year OPERATIONS RESEARCH Time : 3 hours Maximum marks : 75 PART A (5 5 = 25 marks) Answer any FIVE questions. 1. Classify the OR model and explain briefly. 2. Use graphical method to solve Max z 2x1 x2 Subject to the constraints : x1 2x2 x1 x2 6 x1 x2 2 x1 2x 2 x1 , x 2 10 1 0. 3. Describe the Vogel s approximation method. 4. Describe the applications of Goal Programming. 5. Solve the non linear programming problem : 2 2x1 Minimize z 24x1 2 2x 2 8x 2 2 2x 3 12x3 200 Subject to the constraints : x1 x2 x3 x1 , x 2 , x3 11 0. 6. What are the various costs involved in inventory? 7. Two players A and B match coins. If the coins match, then A wins one unit of value, if the coins do not match, then B wins one unit of value. Determine the optimum strategies for the players and the value of the game. PART B (5 10 = 50 marks) Answer any FIVE questions. 8. Use simplex method to solve : Max z x1 x 2 3x3 Subject to the constraints : x1 x2 x3 2x1 x3 2x1 2x 2 x1 , x 2 , x 3 10 2 3x 3 0 0. 2 MCA 766 9. 10. 11. A company is faced with the problem of assigning six different machines to five different jobs. The costs are estimated as follows : Job 1 2 3 4 5 1 2.5 5 1 6 1 22 5 1.5 7 3 Machine 3 3 6.5 2 8 3 4 3.5 7 2 9 4.5 54 7 3 9 6 66 9 5 10 6 Solve the problem assuming that the objective is to minimize total cost. Find the optimum integer solution to the L.P.P. : Max z 2x1 2x 2 Subject to the constraints : 5x1 3x2 8 x1 2x 2 4 x1 , x2 0 and are integers. The profit associated with each of the four activities as a function of the man hours allocated to each is given in the following table. If man hours are available each day, how should the allocation of time be made so that the profit per day is maximized? H: 0123 4 5 6 7 8 g1 (H) : 0 1 3 6 9 12 14 15 16 g2 (H) : 0 2 5 8 11 13 15 16 17 g3 (H) : 0 3 7 10 12 13 13 13 13 g4 (H) : 0 2 5 8 10 10 12 13 14 Use dynamic programming to solve the above problem. 3 MCA 766 12. In a railway marshalling yard, goods trains arrive at a rate of 30 trains per day. Assuming that the inter arrival time follows an exponential distribution and the service time distribution is also exponential with an average 36 minutes. Calculate the following : (a) (b) The probability that the queue size exceeds 10 (c) 13. The mean queue size If the input trains increases to an average 33 per day, what will be the change in (a) and (b)? Solve the following game by using the principle of dominance : Player B I II III IV V VI 14 0 2 1 1 24 3 1 3 2 2 Player A 3 4 3 7 5 1 2 44 3 4 1 2 2 54 14. 2 3 3 2 2 2 Describe the various methods of obtaining random numbers in computer simulation. 4 MCA 766

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