problem1. 

a. Describe linear programming problem? Elucidate the steps involved in the linear programming problem formulation?

b. A paper mill manufactures two grades of paper viz., X and Y. Due to raw material restrictions, it can’t manufacture 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 manufacture 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.
 
problem2. 

a. Discuss the methodology of the Operations Research. 

b. Elucidate in short the phases of Operations Research.

problem3.  Solve the following Linear Programming Problem by using Simple method.
Maximize Z= 3x₁ + 2X₂
Subject to the constraints:
X₁+ X₂ ≤ 4
X₁ - X₂ ≤ 2
X₁, X₂ ≥ 0
 
problem4.  Elucidate the procedure of MODI technique of finding solution through optimality test.
 
problem5. 

a. Elucidate the steps in the Hungarian method.

b. Solve the following assignment problem.

problem6.    

a. Elucidate the steps involved in the Vogel’s approximation method (VAM) of solving Transportation Problem.

b. Solve the following transportation problem using Vogel’s approximation method.