Q. 13

# 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.

Let the firm manufacture x number of Aand y number of B products.

According to the question,

X + y

Maximize Z = 2x + 2y

The feasible region determined by X + y 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

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 Aproducts and 200 number of B products.

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