2015
(May)
MATHEMATICS
(General)
Course: 401
A: (Linear Programming)
Full Marks: 80
Pass Marks: 32
Time: 3 hours
The figures in the margin indicate full marks for the questions
GROUP – A
1. (a) Define convex set. 1
(b) Write the mathematical form of a general linear programming problem. 2
(c) Answer any one question:
 Prove that the intersection of two convex sets is again a convex set.
 A firm produces three types of clothes say A, B and C. Three kinds of wools are required for it, say red wool, green wool and blue wool. One unit length of type A cloth needs 2 meters of red wool and 3 meters of blue wool; one unit length of type B cloth needs 3 meters of red wool, 2 meters of green wool and 2 meters of blue wool; and one unit length of type C cloth needs 5 meters of green wool and 4 meters of blue wool. The firm has only a stock of 8 meters of red wool, 10 meters of green wool and 15 meters of blue wool. It is assumed that the income obtained from the one unit length of type A cloth is Rs. 3, of type B cloth is Rs. 5, and that of type of C cloth is Rs. 4. Formulate the problem as linear programming problem.
(d) Answer any one question:
 Solve graphically the following LPP:
Maximize
Subject to
And
 Solve graphically the following LPP:
Minimize
Subject to
And
2. (a) What do you mean by ‘feasible solution’ of linear programming problem?
(b) Define slack and surplus variables of a linear programming problem.
(c) Answer any one question:
 Using the simplex method, solve the linear programming problem:
Minimize
Subject to
And
 Discuss the computational procedure of simplex method to solve a linear programming problem.
(d) Answer any one question: 8
 Solve the LPP using twophase method:
Minimize
Subject to
And
 Using BigM method, solve the following LPP:
Minimize
Subject to
And
3. (a) Write true or false: The dual of a maximization problem is a minimization problem. 1
(b) What do you mean by symmetric primal dual and unsymmetric primal dual and unsymmetric primal dual problems? 2
(c) Answer any one question: 5
 Set up the dual of the following primal problem:
Minimize
Subject to
And
is unrestricted in sign.
 Prove that dual of the dual of a given primal is the primal itself.
4. (a) Answer the following questions: 1x2=2
 Define unbalanced transportation problem.
 Define feasible solution of transportation problem.
(b) Define different types of basic feasible solution. 2
5. Answer any one question: 8
 Obtain an optimal solution using Vogel’s method:
Supply
 
19

30

50

10

7
 
70

30

40

60

9
 
40

8

70

20

18
 
Demand

5

8

7

14

34

 Write short notes on:
 NorthWest corner rule.
 Vogel’s approximation method.