problem1)

a) What do you understand by linear programming problem? describe the steps involved in linear programming problem formulation briefly?
b) The paper mill produces two grades of paper i.e. X and Y. Because of raw material restrictions, it can’t produce 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. Mill earns a profit of Rs. 200 and Rs. 500 per ton of grade X and Y paper respectively. Formulate this as Linear Programming Problem.      

problem2)    

a) Discuss the methodology of Operations Research.
b) Describe in brief the phases of Operations Research.

problem3)

Solve following Linear Programming Problem using simple method.
Maximize Z= 3x1 + 2X2
Subject to the constraints:
X1+ X2 ≤ 4
X1 - X2 ≤ 2
X1, X2 ≥ 0    

problem4) describe the procedure of MODI method of finding solution through optimality test.    

problem5)

a) describe the steps in Hungarian method.
b) Solve assignment problem given below:

Machine      Operators
 1            2        3       4        5
 A            60     50      45      45
 B            40     45      55      35
 C            55     70      60      50
 D            45     45      40      45

problem6)

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 Centres           Supply
                        C1      C2      C3      C4
 F1                     3        2       7        6        50
 F2                     7        5       2        3        60
 F3                     2        5       4        5        25
 Requirements      60      40      20      15