Monday, December 31, 2018

Dibrugarh University Arts Question Papers:MATHEMATICS (A: Linear Programming)' (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.


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