Question

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 1

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

∴According to the question,

360x + 240y ≤ 5760,x + y ≤ 20, x ≥ 0, y ≥ 0

Maximize Z = 22x + 18y

The feasible region determined by 360x + 240y ≤ 5760,x + y ≤ 20, x ≥ 0, y ≥ 0 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

Corner Point	Z = 22x + 18y
A(0, 0)	0
B(0, 20)	360
C(8, 12)	392	Maximum
D(16, 0)	352

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.