## Saturday, April 21, 2018

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
1. Prove that the intersection of two convex sets is again a convex set.
2. What are the limitations of LP model?
(d) Answer any one question: 5
1. Solve graphically the following LPP:
Maximize
Subject to
And
1. 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
1. Using the simplex methods, solve the linear programming problem.
Maximize
Subject to
And
1. Discuss the computational procedure of simplex method to solve a linear programming problem.
(d) Answer either (i) or (ii): 8
1. Solve the following LPP using two-phase method:
Maximize
Subject to
And
1. Using Big-M 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
1. Obtain the dual problem of the following primal LP problem:
Minimize
Subject to
And
1. Prove that dual of the dual of a given primal problem is the primal itself.
4. (a) Answer the following questions: 1x2=2
1. Define unbalanced transportation problem.
2. Define feasible solution of transportation problem.
3. Write the mathematical formulation of a transportation problem.
5. Answer any one question: 8
1. 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

1. Write short notes on:

1. North-West corner rule.
2. Least cost method.