Question

a) A firm manufacturers three products A, and B C . The profit on these products are `
3, ` 2, ` 4 respectively. The firm has two machines and the required processing time
in minutes for each machine on each product is given below.

Product
A B C
Machine X 4 3 5
Y 2 2 4
Machine X and Y have 2000 and 1500 minutes respectively. The firm must
manufacture 100 A’s, 200 B’s and 50 C’s but no more than 150 A’s. Set up an L.P.
model to maximize the profit. Solve the problem graphically. (6)
b) Write the dual of the following LPP:
1 2 3 max Z = 2x + 3x −5x
Subject to
2 2 3 x1 + x2 − x3 ≤
3 3 4 x1 + x2 − x3 ≤
4 5 7 6 x1 + x2 − x3 =
and , 0 x1
x2 ≥ , and 3
x unrestricted.