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, M_{1} and M_{2}. Type A requires one minute of processing time on M_{1} and two minutes on M_{2}. Type B requires one minute on M_{1} and one minute on M_{2} is available for not more than 6 hours 40 minutes while M_{2} 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 :

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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PREVIOUSA dealer wishes to purchase a number of fans and sewing machines. He has only ₹5760 to invest and space for at most 20 items. A fan costs him ₹360 and a sewing machine, ₹240. He expects to gain ₹22 on a fan and ₹18 on a sewing machine. Assuming that he can sell all the items he can buy, how should he invest the money in order to maximize the profit?NEXTA 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.

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