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Saturday, April 21, 2018

BA 4th Semester Question Papers: Mathematics (May' 2017)

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.

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