Kerala University 2005 B.C.A Computer Application operation research - Question Paper
Reg. No.....................................................(Pages : 4) K 5183
Name...____..............................
SIXTH SEMESTER B.C.A. DEGREE EXAMINATION, MARCH/APRIL 2005
(Vocational Course)
Optional Subject : Mathematics Paper XIIOPERATIONS RESEARCH Time : Three Hours Maximum : 90 Marks
Unit I
{Maximum: 40 marks)
1. Prove the following :
(a) Every hyperplane is a convex set. (3 marks)
(b) The intersection of two convex sets is also a convex set. (4 marks)
4. Use dual simplex method to solve the following L.P.P.:
" Maximize Z = - 2xj - 2x2 - 4*3
subject to the constraints
3&0 + 5*o >
2
3
5
7ac3 <
c2 +
*2 + 4x2 + xv x2, xs 0.
6x3
(10 marks)
5. Use simplex method to solve the following L.P.P. Maximize Z = ar1 + 2x2 subject to the constraints
10
40
*1 + 2x1 -
x2 0-
(10 marks) (5 marks)
6. State and prove the fundamental theorem of duality.
7. Use Big-M method to
Maximize Z = 3x: + 2x2 + 3x3 subject to the constraints :
2xj +
x3 <
x2 +
3*! + 4x2 + 2x3 > 8
xlt x2, x3 0.
(10 marks)
(Maximum : 40 marks)
8. Determine an initial basic feasible solution to the following transportation problem using the North-West comer rules:
Availability
|
Di |
d3 |
d4 | |||
|
1 |
6 |
4 |
1 |
5 |
14 |
|
02 |
8 |
9 |
2 |
7 |
16 |
|
Os |
4 |
3 |
6 |
2 |
5 |
|
6 |
10 |
15 |
4 |
Requirement
where Oi and D, represent the Ith origin and 7th destination respectively.
(7 marks)
9. Obtain an initial basic feasible solution to the following T.P. using Vogels approximation method :
|
Warehouses |
Stores |
Availability | |||
|
I |
II |
III |
IV | ||
|
A |
5 |
1 |
3 |
3 |
34 |
|
B |
3 |
3 |
5 |
4 |
15 |
|
C |
6 |
4 |
4 |
3 |
12 |
|
D |
4 |
-1 |
4 |
2 |
19 |
|
Requirement |
21 |
25 |
17 |
17 |
80 |
(8 marks)
10. State the assignment problem. Describe an algorithm for the solution of the assignment problem.
(7 marks)
11. Consider the problem of assigning five jobs to five persons. The assignment costs are given as follows :
|
Persons |
Jobs | ||||
|
1 |
2 |
3 |
4 |
5 | |
|
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 |
Determine the optimum assignment schedule.
(8 marks)
12. Solve the following 2x3 game graphically.
|
PlayerB | ||||||||||||
|
(8 marks)
13. Using dominance properly, solve the game whose payoff matrix is given by :
|
PlayerB | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
(7 marks) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
15. The following table gives the running cost per year and resale price of certain equipment, whose, purchase price is Rs. 5,000 :
|
Year |
1 |
2 |
S |
4 |
5 |
6 |
7 |
8 |
|
Running cost (Rs.) |
1,500 |
1,600 |
1,800 |
2,100 |
2,500 |
2,900 |
3,400 |
4,000 |
|
Resale value (Rs.) |
3,500 |
2,500 |
1,700 |
1,200 |
800 |
500 |
500 |
500 |
At what year is the replacement due.
(8 marks)
Unit m
(Maximum : 10 marks ; 2 marks each)
16. Define Slack variables.
17. Mention the rules for dominance.
18. Define a quadratic form.
19. Write the standard form of the following L.P.P.:
Minimize Z = 2* + 4y subject to the constraints
2x + y 3 x - y 2: 4 x + 2y = 5 x,yZ 0.
. 20. What is degeneracy in Transportation problem ?
|
Attachment: |
| Earning: Approval pending. |
