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Sunday, April 30, 2017

Dibrugarh University (BA - 4th Semester) Question Papers - Mathematics General (May' 2014)

2014
(May)
MATHEMATICS
(General)
Course: 401
(A: Linear Programming)
Full Marks: 50
Pass Marks: 20
Time: 2 ½ hours
The figures in the margin indicate full marks for the questions
(GROUP – A)

1. (a) Define hypersphere. 1
(b) What are four basic assumptions necessary for linear programming model? 2
(c) Answer any one question: 4
  1. What are the limitations of LP model?
  2. Prove that hyperplane is a convex set.
(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 ‘decision variable’ in linear programming problem? 1
(b) Mention the difference between ‘feasible solution’ and ‘basic feasible solution’ in a linear programming problem. 2
(c) Using simplex method, solve any one of the following LPP: 7
  1. Maximize
Subject to
And
  1. Minimize
Subject to
And
(d) Answer either (i) or (ii): 8
  1. Solve LPP using two-phase method:
Maximize
Subject to
And
  1. Using Big-M method, solve the following LPP:
Maximize
Subject to
And
3. (a) What is ‘dual’ linear programming problem? 1
(b) Write the dual of the following LPP: 2
Maximize
Subject to
And
(c) Answer any one question: 5
  1. Find the dual of the primal:
Maximize
Subject to
And
  1. Ifbe any feasible solution to the primal max, subject to andbe any feasible solution to its dual, minsubject tothen show that.
4. (a) Answer the following questions: 1x2=2
  1. Define ‘loop’ in a transportation problem.
  2. How many decision variables will be there in transportation problem containing m-sources and n-destinations?
(b) Write the mathematical formulation of a transportation problem. 2
5. Answer any one question: 8
(a) Determine an initial basic feasible solution using northwest-corner method and least cost method, and compare their corresponding costs:

Supply
4
6
9
5
16
2
6
4
1
12
5
7
2
9
15
Demand
12
14
9
8
43

(b) Write short notes on Vogel’s approximation method.
(c) Prove that, in a balanced transportation problem having-origin and-destinationsthe exact number of basic variables is.