2016

(November)

MATHEMATICS

(General)

Course: 401

A: (Linear Programming)

Full Marks: 80

Pass Marks: 20 / 15

Time: 2 ½ hours

The figures in the margin indicate full marks for the questions

(b) Write two limitations of LP model. 2

(c) Answer any one question: 4

- Prove that the set of all feasible solutions to an , is closed convex set.
- A manufacturer produces two types of models and. Each model requires 4 hours of grinding and 2 hours of polishing; whereas each model requires 2 hours of grinding and 5 hours of polishing. The manufacturer has 2 grinders and 3 polishers. Each grinder works for 40 hours a week and each polisher works for 60 hours a week. Profit on an model is Rs. 3 and on an model is Rs. 4. Whatever is produced in a week is sold in the market. How should the manufacturer allocate his production capacity to the two types of models so that he may make the maximum profit in a week?

(d) Solve graphically any one of the following:

- Maximize

Subject to

And

- Minimize

Subject to

And

2. (a) Who developed the solution of LPP using simplex method? 1

(b) Mention the difference between ‘feasible solution’ and ‘basic feasible solution’ in an LPP. 2

(c) Using simplex method, solve any one of the following LPP: 7

- Maximize

Subject to

And

- Minimize

Subject to

And

(d) Answer either (i) or (ii):

- Solve the following using two-phase method:

Minimize

Subject to

and

- Using Big-M method, solve the following :

Minimize

Subject to

and

3. (a) If the variable in primal is unrestricted in sign, then what about the dual constraint? 1

(b) Write two advantages of duality. 2

(c) Answer any one question: 5

- Obtain the dual problem of the following primal LP problem:

Minimize

Subject to

And

- Prove that if the primal problem has an unbounded solution, then the dual problem has either no solution or an unbounded solution.

4. (a) Answer the following questions: 1x2=2

- What do you mean by a balanced transportation problem?
- Define loop of a transportation table.

(b) Write the mathematical formulation of transportation problem. 2

5. Answer any one question: 8

- Solve the following transportation problem using ‘least cost method’:

Supply | |||||

1 | 2 | 1 | 4 | 30 | |

3 | 3 | 2 | 1 | 50 | |

4 | 2 | 5 | 9 | 20 | |

Demand | 20 | 40 | 30 | 10 | 100 |

- Write a short note on Vogel’s approximation. 4
- Prove that there exists a feasible solution in each transportation problem, which is given by

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