A chain saw requires 2 hours of assembly and a wood chipper

A chain saw requires 2 hours of assembly and a wood chipper 4 hours. A maximum of 16 hours of assembly time is available. The profit is $180 on a chain saw and $240 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 x chain saws and y wood chippers are assembled.

2x + 4y 16 ... (1)

x 0, y 0

max (180 x + 240 y)   

when we draw line 1 on co-ordinate axis ,

we have a triangular feasible region with vertices

A(0,0) , B(8,0) ,C(0,4)

profit at A = 0 *180 + 0 * 240 = 0

profit at B = 8 *180 + 0 * 240 = 1440

profit at C = 0 *180 + 4* 240 = 960

hence for maximum profit 8 chain saws are made and no wood chippers are assembled..