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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]     

  1. 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
                          x1, 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]







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