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

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wk7 MCA 141 MCA 16 M.C.A. DEGREE EXAMINATION JANUARY, 2009. Fourth Semester/Second Year OPERATIONS RESEARCH Time : 3 hours Maximum marks : 75 Answer for 5 marks question should not exceed 2 pages. Answer for 10 marks questions should not exceed 5 pages. PART A (5 5 = 25 marks) Answer any FIVE questions. 1. What is sample space? What are the different types of sample space? 2. Define slack and surplus variable. 3. What do you mean by unbalanced transportation problem? Give an example. 4. State Bellman's principle of optimality. 5. List out the applications of Goal programming. 6. Why inventory should be maintained? 7. What is two-person zero-sum game? wk7 PART B (5 10 = 50 marks) Answer any FIVE questions. 8. Use simplex method to Minimize z x1 3 x2 2x3 subject to the constraints : 3 x1 2x3 7 2x1 4x2 12 3 x2 8 x3 10 x1 , x2 , x3 4 x1 x2 0. 9. Five jobs are to be processed and five machines are available. Any machine can process any job with the resulting profit (in rupees) as follows : Machine ABCD E 1 32 38 40 28 40 2 40 24 28 21 36 Job 3 41 27 33 30 37 4 22 38 41 36 36 5 29 33 40 35 39 What is the maximum profit that may be expected if an optimum assignment is made? 2 MCA 141 wk7 10. Use dynamic programming to find the value of Maximize Z y1 , y2 , y3 subject to the constrains : y1 y3 5 y1 , y2 , y3 11. y2 0. Solve the non-linear programming problem : Minimize Z 2 2x1 24 x1 2 2x 2 8 x2 2 2 x3 12x3 200 subject to the constraints : x1 x2 x3 x1 , x2 , x3 11 0. 12. At a one man barber shop customers arrive according to Poisson distribution with a mean arrival rate of 5 per hour and his hair cutting time was exponentially distributed with an average hair cut taking 10 minutes. Calculate the following : (a) Average number of customers in the shop and the average number of customers waiting for hair cut. (b) The percentage of time an arrival can walk right in without having to wait. 3 MCA 141 wk7 13. Solve the following game Player B II III IV V VI 14 2 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 3 3 2 2 2 I 14. The demand for a particular item is 18000 units per year. The holding cost per unit is Rs. 1.20 per year and the cost of one procurement is Rs. 400. Determine : (a) Optimum order quantity (b) Time between orders and (c) is Re. 1. Total cost per year when the cost of one unit 4 MCA 141

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