Optimization Theory Sample paper

1. What is operations research? Explain the scope of OR.                                    [3]
2. List the phases of OR and explain them.                                                           [3]
3. Discuss the guideline of formulation of Linear Programming model and for 

       converting it into standard form?                                                                          [3]     

4. Define the following:                                                                                         [3]

            a.  Optimal solution.

                   b. Unbounded solution.

c.   Artificial variable.

      5. A paper mill produces 2 grades of paper namely X and Y. Because of raw  material restrictions, it cannot produce more than 400 tonnes of grade X and 300            tonnes of grade Y in a week. There are 160 production hours in a week. It requires 0.2 and 0.4 hours to produce a ton of products X and Y respectively with corresponding profits of Rs.200 and Rs. 500 per ton. Formulate the above as a LPP to maximize profit and find the optimum product mix.                                     [3]

6. What conditions must exist in a simplex table to establish the existence of an alternative solution? Unbounded solution?  Degeneracy?                                     [3]

7.  Solve following LP problem using Big M method:

Maximize Z=3x₁ + 5x₂

subject to constraints

                        x₁-2x₂ ≤6

                               x₁≤10

                               x₂≥1

                          x_1, x₂ ≥0                                                                                    [3]

8. What are artificial variables? Why do we need them? Describe two- phase

     method of solving LP problem with artificial variables.                                   [3]

9.  XYZ company produces automobile spare part. The contract that it has signed

     with a large truck manufacturer calls for the following 4-month shipping   

     schedule:

        

Month	Number of parts to be shipped
January	3000
Feburary	4000
March	5000
April	5000

           The company can manufacture 3000 parts per month on a regular time basis             

           and  2000 parts per month on overtime basis. Its production cost is Rs 15000 for

           a part  produced in regular time and 25000 for part produced in overtime.            

           Formulate   problem as LP model to minimize overall cost.                            [3]

     10.  What are unrestricted variables? How can we solve a Linear Programming

          problem having unrestricted variable using simple method? Explain with 

          example.                                                                                                             [3]