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TAMIL NADU OPEN UNIVERSITY MCA - II (SEM 4) JUN 2009 : Operation Research

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Ws 6 MCA-426 MCA 16 M.C.A. DEGREE EXAMINATION JUNE 2009. Fourth Semester / Second Year OPERATIONS RESEARCH Time : 3 hours Maximum marks : 75 PART A (5 5 = 25 marks) Answer any FIVE questions. 1. Classify the OR models of structure. 2. Use graphical method to solve : Maximize z 2x1 x2 subject to the constraints : x1 2x 2 10 x1 x2 6 x1 x2 2 2x 2 1 x1 x1 , x 2 0. Ws 6 3. Write the mathematical Assignment Problem. formulation 4. Define (a) All IPP (b) Mixed IPP. 5. Describe the characteristics of queueing system. 6. Write the advantages of simulation. 7. of Obtain the necessary conditions for the NLPP : 2 x1 Maximize z 2 3x 2 2 5x 3 subject to the constraints : x1 3x3 2 2x 2 x3 5 x1 , x 2 , x 3 5x1 x2 0. PART B (5 10 = 50 marks) Answer any FIVE questions. 8. Use Simplex method to Maximize z 3x1 5x2 subject to the constraints : 3x1 2x 2 18 x1 4 x2 6 x1 , x2 0. 2 MCA-426 Ws 6 9. Obtain an optimum basic feasible solution to the following Transportation Problem : Warehouse W1 W2 W3 W4 F1 19 30 50 10 7 Factory F2 70 30 40 60 9 F3 40 8 70 20 18 5 8 7 14 Capacity Requirements 10. Find the Optimum integer solution to the LPP using Gomory's constraint : Maximize z 2x1 2x2 Subject to the constraints : 5x1 3x 2 8 x1 2x 2 4 x1 , x 2 0 and are integers. 11. Use the Khun-Tucker conditions to solve the following NLPP : Maximize z 2 2x1 2x1 x 2 2 7x2 subject to the constraints : 2 x1 5x 2 98 x1 , x 2 0. 3 MCA-426 Ws 6 12. Consider the EOQ system : Annual consumption is 12000 units at the cost of Rs. 7.50 per unit. Set-up cost is Rs. 6 and the average inventory holding cost is Rs. 0.90 per unit. Normal lead time is 15 days and maximum lead time is 20 days. Calculate the following : (a) Optimal order quantity (b) Time between order (c) Buffer stock (d) ROL. 13. Given an arrival rate of 20 per hour, is it better for a customer to get service at a single channel with mean service rate of 22 customers or at one of two channels in parallel, with mean service rate of 11 customers for each of the two channels? Assume both the queues are M/M/S type. 14. A and B play game in which each has three coins, a 5 paise, a 10 paise and a 20 paise. Each selects a coin without the knowledge of the other's choice. If the sum of the coins is an odd amount, A wins B's coin, if the sum is even, B wins A's coin. Find the best strategy for each player and the value of the game. 4 MCA-426

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Additional Info : Mca - II (sem 4) June 2009 Question Paper - Operation Research
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