## Monday, December 31, 2018

2013
(May)
MATHEMATICS
(General)
Course: 401
(A: Linear Programming)
(Group – A)
Full Marks: 50
Pass Marks: 20
Time: 2 ½   hours
The figures in the margin indicate full marks for the questions

1. (a) Define convex set. 1
(b) Write two advantages of linear programming techniques. 2
(c) Answer any one question: 4
1. Prove that the intersection of two convex sets is again a convex set.
2. Discuss the graphical method of solving a linear programming problem.
(d) Answer any one question: 5
1. Solve graphically the following:
Minimize
Subject to

And
1. Solve graphically the following:
Minimize
Subject to

And
2. (a) Who developed the solution of using simplex method? 1
(b) Define slack and surplus variables of a linear programming problem. 2
(c) Answer any one question: 7
1. Using the simplex method, 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 theusing two-phase method:
Minimize
Subject to

And
1. Using Big-M method, solve the following
Minimize
Subject to

And
3. (a) Write true or false: The dual of a maximization problem is a minimization problem. 1
(b) Write the ‘dual’ of the following: 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 is the primal itself.
4. (a) Answer the following questions: 1x2=2
1. What do you mean by a balanced transportation problem?
2. Define feasible solution of a transportation problem.
(b) Write the necessary and sufficient condition for the existence of a feasible solution to a transportation problem. 2
5. Answer any one question: 8
(a) 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

(b) Write short notes on:
1. North-West corner rule.
2. Least cost method.

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