## Monday, December 31, 2018

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. If be any feasible solution to the primal max , subject to and be any feasible solution to its dual, min subject to then 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 -destinations the exact number of basic variables is .

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