2017
(May)
MATHEMATICS
(General)
Course: 401
A: (Linear Programming)
Full marks: 50
Pass Marks: 20/15
Time: 2 ½ hours
The figures in the margin indicate full marks for the questions
1. (a) Define hypersphere. 1
(b) Write the mathematical form of a general linear programming problem. 2
(c) Answer any one question: 4
 Prove that the intersection of two convex sets is again a convex set.
 What are the limitations of LP model?
(d) Answer any one question: 5
 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? 1
(b) Define slack and surplus variable of a linear programming problem. 2
(c) Answer any one question: 7
 Using the simplex methods, solve the linear programming problem.
Maximize
Subject to
And
 Discuss the computational procedure of simplex method to solve a linear programming problem.
(d) Answer either (i) or (ii): 8
 Solve the following LPP using twophase method:
Maximize
Subject to
And
 Using BigM method, solve the following LPP:
Minimize
Subject to
And
3. (a) Write True or False: 1
The dual of a maximization problem is a minimization problem.
(b) Write the dual of the following LPP: 2
Maximize
Subject to
And
(c) Answer any one question: 5
 Obtain the dual problem of the following primal LP problem:
Minimize
Subject to
And
 Prove that dual of the dual of a given primal problem is the primal itself.
4. (a) Answer the following questions: 1x2=2
 Define unbalanced transportation problem.
 Define feasible solution of transportation problem.
 Write the mathematical formulation of a transportation problem.
5. Answer any one question: 8
 Obtain an optimal solution using Vogel’s method of the following transportation problem:
D1

D2

D3

D4

Supply
 
S1

19

30

50

10

7

S2

70

30

40

60

9

S3

40

8

70

20

18

Demand

5

8

7

14

34

 Write short notes on:
 NorthWest corner rule.
 Least cost method.