Q. 38

A dealer wishes to purchase a number of fans and sewing machines. He has only ₹5760 to invest and has space for at most 20 items. A fan costs him ₹360 and a sewing machine ₹240. He expects to sell a fan at a profit of ₹22 and a sewing machine at a profit of ₹18. Assuming that he can sell all the items that he buys, how should he invest his money to maximize the profit? Solve the graphically and find the maximum profit.

Answer :

Let the number of fans bought be x and sewing machines bought be y.

According to the question,

360x + 240y,x + y

Maximize Z = 22x + 18y

The feasible region determined by 360x + 240y,x + y is given by

The corner points of the feasible region are A(0,0) , B(0,20),C(8,12) , D(16,0).The value of Z at corner points is

The maximum value of Z is 392 at point (8,12).

The dealer must buy 8 fans and 12 sewing machines to make the maximum profit.

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