A chain saw requires 8 hours of assembly and a wood chapper

A chain saw requires 8 hours of assembly and a wood chapper 7 hours. A maximum of 112 hours of assembly time is available. The profit is $190 on a chain saw and $250 on a chipper. How many of each should be assembled for maximum profit? To attain the maximum profit, assemble chain saws and wood chippers.

Solution

Let number of chain saw be x

Let number of wood chipper be y

Total hours : 8x +7y<= 112 hrs

Further x>=0 and y>0

Profit function, P(x,y) = $190x +$250y = 190x +250y

The inequality : 8x +7y <= 112

The vertex poinst of the graph are ( 14, 0) and ( 0, 16)

Check the Proft on these points: P(x, y) = at ( 14, 0) P = 190*14 +0 = $2660

at ( 0, 16) P = 0 +250*16 = $4000

We can see maximim profit occurs at Chain saw = 0 numbers ; wood chipper = 16 numbers