Q1. a) What do you understand by linear programming problem? Describe the steps involved in linear programming problem formulation?
b) Paper mill produces two grades of paper viz., X and Y. As of raw material restrictions, it can’t generate more than 400 tons of grade X paper and 300 tons of grade Y paper in a week. There are 160 production hours in a week. It needs 0.20 and 0.40 hours to produce a ton of grade X and Y papers. The mill earns a profit of Rs. 200 and Rs. 500 per ton of grade X and Y paper respectively. Formulate this as a Linear Programming Problem.
Q2.a) Discuss the methodology of Operations Research.
b) Describe in brief the phases of Operations Research.
Q3) Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x1 + 2X2 Subject to the constraint
X1+ X2 ≤ 4
X1 - X2 ≤ 2
X1, X2 ≥ 0
Q4) Describe the procedure of MODI method of finding solution through optimality test.
Q5. a) Describe the steps in Hungarian method.
b) Solve the following assignment problem.
Machine Operators
1 2 3 5
A 60 50 45 45
B 40 45 55 35
C 55 70 60 50
D 45 45 40 45
Q6. a) Describe the steps involved in Vogel’s approximation method (VAM) of solving Transportation Problem.
b) Solve the following transportation problem using Vogel’s approximation method.
Factories Distribution Centre Supply
C1 C2 C3 C4
F1 3 2 7 6 50
F2 7 5 2 3 60
F3 2 5 4 5 25
Requirements60 40 20 15