Question

A firm manufactures two types of products, A and B, and sells them at a profit of₹2 on type A and ₹2 on type B. Each product is processed on two machines, M1 and M2. Type A requires one minute of processing time on M1 and two minutes on M2. Type B requires one minute on M1 and one minute on M2 is available for not more than 6 hours 40 minutes while M2 is available for at most 10 hours a day. 

Find how many products of each type the firm should produce each day in order to get maximum profit.

Answer 1

Let the firm manufacture x number of A and y number of B products. 

∴According to the question, 

X + y ≤ 400, 2x + y ≤ 600, x ≥ 0,y ≥ 0

Maximize Z = 2x + 2y

The feasible region determined by X + y ≤ 400, 2x + y ≤ 600, x ≥ 0, y ≥ 0 is given by

The corner points of feasible region are A(0,0) , B(0,400) , C(200,200) , D(300,0).

The value of Z at corner point is

Corner Point	Z = 2x + 2y
A(0, 0)	0
B(0, 400)	800	Maximum
C(200, 200)	800	Maximum
D(300, 0)	600

The maximum value of Z is 800 and occurs at two points. Hence the line BC is a feasible solution. 

The firm should produce 200 number of A products and 200 number of B products.