[BA 4th Sem Question Papers, Dibrugarh University, 2013, Mathematics, General, A: Linear Programming]
1. (a) Define convex set. 1
(b) Write two advantages of linear programming techniques. 2
(c) Answer any one question: 4
- Prove that the intersection of two convex sets is again a convex set.
- Discuss the graphical method of solving a linear programming problem.
(d) Answer any one question: 5
- Solve graphically the following
:
Minimize
Subject to
And 
- Solve graphically the following
Minimize 
Subject to
And 
2. (a) Who developed the solution of using simplex method? 1
using simplex method? 1
(b) Define slack and surplus variables of a linear programming problem. 2
(c) Answer any one question: 7
- Using the simplex method, 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
using two-phase method:
Minimize 
Subject to
And 
- 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
: 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 is the primal itself.
4. (a) Answer the following questions: 1x2=2
- What do you mean by a balanced transportation problem?
- 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
Also Read: Dibrugarh University Question Papers
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:
- North-West corner rule.
- Least cost method.
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