- What is operations research? Explain the scope of OR. [3]
- List the phases of OR and explain them. [3]
- Discuss the guideline of formulation of Linear Programming model and for
converting it into standard form? [3]
- 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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