Question

A dealer wishes to purchase a number of fans and radios. He has Rs. 5,760 to invest and has a space for at most 20 items. A fan costs him Rs. 360 and a radio Rs. 240. His expectation is that he can sell a fan at a profit of Rs. 22 and a radio at a profit of Rs. 18. Assuming that he can sell and the items he buys, how should he invest his money to get maximum profit ? Translate the problem as LPP and solve is graphically.

Answer 1

Let number of fans = x

and number of radios = y

max. profit z = 22x + 18y

according to constraints

x + y ≤ 20

360x + 240y ≤ 5,760

Now plot the straight lines on the graph and find the corner points of feasible region

∴ Corner points of feasible region are A(16, 0), P(8, 12) and C(0, 20) Corner points Z = 22x + 18y

A(16, 0) Z = 352 + 0 = 352

P(8, 12) Z = 176 + 216 = 392

e(0, 20) Z = 0 + 360 = 360

∴ Max. profit Z = Rs. 392 at x = 8, y = 12.