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KERALA UNIVERSITY MCA - II (SEM 3) MAY 2009 : Numerical Analysis And Optimization Techniques

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*1884* 1884 (Pages : 3) Reg. No. : ..................................... Name : .......................................... Third Semester M.C.A. Degree Examination, May 2009 06.303 : NUMERICAL ANALYSIS AND OPTIMIZATION TECHNIQUES Time : 3 Hours Max. Marks : 100 PART A Answer all questions. Each question carries 4 marks. 1. What are Inherent errors and Truncation errors in numerical calculations ? 2. Find the root of the equation xex 3 = 0, lies between 1 and 2, by False Position. 3. How to find the ! # by iteration ? 4. What is difference between objectives and constraints ? 5. Explain the artificial variable technique. 6. Define canonical form. 7. What is basic feasible solution ? 8. Explain significance of duality in linear programming application. 9. What is slack and surplus variables ? 10. Explain dual simplex method. (10 4=40 Marks) PART B Answer any two questions from each Module. Each question carries 10 marks. Module I 11. a) Find positive root of the equation nex = 1 between 0 and 1. b) Evaluate root of the equation x = e 2x by Newton Raphson method. P.T.O. 1 884 *1884* -2- 12. a) Derive Newton s backward difference interpolation formula. b) Some values of x and log10(x) are (300, 2.4771), (304, 2.4829), (305, 2.4843) and (307, 2.4871). Find log10 (301). 13. The table gives distances in nautical miles of the visible Horizon for the given heights in feet above earth s surface Height (x) : 100 10.63 Distance (y) : 150 13.03 200 250 15.04 16.81 300 350 18.42 19.9 Find values of y when x = 218 and 360 ft. Module II 14. Maximize x1 + 3x2 + 3x3 x4 Subject to constraints : x1 + 2x2 + 3x3 = 15 2x1 + x2 + 5x3 = 20 x1 + 2x 2 + x3 + x 4 = 10 where x1, x2, x3 and x4 are all positive. 15. Using the Duality method of solution, Maximize Z = 5x1 2x 2 + 3x3 such that 2x1 + 2x2 x3 3x1 4x2 x2 + 2x3 x1, x2, x3 2 3 5 and 0. 16. A mobile company manufactures two models. Daily capacity of Model A is 150 and that of Model B is 160. For the type A the unit uses 16 discrete components and for type B 21 discrete components. The maximum daily availability of components is 1020. The profit per model A and B are Rs. 250 and Rs. 300 respectively. Formulate the problem as LPP and solve by graphically to find optimum daily production. *1884* 1884 -3- Module III 17. Solve the Assignment problem. 1 ) 1 1 & * 1 8 # & " - 1 # " ' ! ' 8 $ ' ! , 1 " + 1 $ # & ! ' # 18. For the transport network find the maximum flow : 19. Find an initial basic feasible solution to the following transportation problem. Also show that this solution is the optimum solution. D D D D O D ! % % " ! S " # u p p l y # " # O O ' # & $ $ ! ' % # ' # $ ! % # ! O ! . " O # " # $ D # e m a n d 2 0 8 0 5 0 7 5 8 5 # (10 6=60 Marks)

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Additional Info : Mca - II (sem 3) May 2009 Question Paper - Numerical Analysis And Optimization Techniques
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