Kerala University 2009-3rd Sem M.C.A NUMERICAL ANALYSIS AND OPTIMIZATION TECHNIQUES - Question Paper
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IUVVRH (Pages : 3) 1884
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 a 0, lies between 1 and 2, by False - Position.
3. How to find the 3/5 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. (10x4=40 Marks)
PART - B
Answer any two questions from each Module. Each question carries 10 marks.
11. a) Find positive root of the equation nex a 1 between 0 and 1.
b) Evaluate root of the equation x a e-2x by Newton - Raphson method.
12. a) Derive Newtons 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 logi0 (301).
13. The table gives distances in nautical miles of the visible Horizon for the given heights in feet above earths surface
Height (x) : 100 150 200 250 300 350 Distance (y) : 10.63 13.03 15.04 16.81 18.42 19.9 Find values of y when x a 218 and 360 ft.
14. Maximize X1 + 3x2 + 3x3 - X4 Subject to constraints :
x1 + 2x2 + 3x3 a 15 2x1 + x2 + 5x3 a 20 x1 + 2x2 + x3 + x4 a 10 where x x2, x3 and x4 are all positive.
15. Using the Duality method of solution,
Maximize Z a 5x1 - 2x2 + 3x3
such that
2x1 + 2x2 - x3 2 3x1 - 4x2 3 x2 + 2x3 < 5 and x x2, x3 > 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.
17. Solve the Assignment problem.
|
I |
II |
III |
IV |
V | |
|
A |
8 |
4 |
2 |
6 |
1 |
|
B |
0 |
9 |
5 |
5 |
4 |
|
C |
3 |
8 |
9 |
2 |
6 |
|
D |
4 |
3 |
1 |
0 |
3 |
|
E |
9 |
5 |
8 |
9 |
5 |
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, |
Supply | |||||
|
O i |
7 |
7 |
10 |
5 |
11 |
45 |
|
4 |
3 |
5 |
6 |
13 |
90 | |
|
9 |
8 |
6 |
7 |
5 |
95 | |
|
o 4 |
12 |
13 |
10 |
6 |
3 |
75 |
|
5 |
5 |
4 |
5 |
6 |
12 |
05 |
|
Demand |
20 |
80 |
50 |
75 |
85 |
(10x6=60 Marks)
|
Attachment: |
| Earning: Approval pending. |
