Question

A firm owned by Sheshnag manufactures two types of products A and B and sell them at a profit of Rs 2 on type of A and 3 on type B. Each product is processed on machines M₁ and M₂. Type A requires one minute of processing time on M₁ and two minutes on M₂. Type B requires one minute of time on M₁ and one minute on M₂. The machine M₁ is available for not more than 6 hours 40 minutes while M₂ is available for 10 hours during any working day. Formulate the L.P.P. in order to find how many products of each type, should the firm produce each day so that profit is maximum.

Answer 1

Let the number of units of product A be x & product B be y

	A	B	Available
Machine 1	1	1	not more than 6 hours minimum
Machine 2	2	1	10 hours
Profit	2	3

Maximize z = 2x + 3y 

subject to the constraints [6 hrs + 40 minutes 360 minutes + 40 minutes = 400 minutes] 

x + y ≤ 400 

2x + y ≤ 600 

x, y ≥ 0