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Sunday, April 30, 2017

Dibrugarh University (BA - 4th Semester) Question Papers - Mathematics General (May' 2013)

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.