A chain saw requires 6 hours of assembly and a wood chipper 4 hours. A maximum of 48 hours of assembly time is available. The profit is $ 190 on a chain saw and $ 220 on a chipper. How many of each should be assembled for maximum profit?

Question

A chain saw requires 6 hours of assembly and a wood chipper 4 hours. A maximum of 48 hours of assembly time is available. The profit is $ 190 on a chain saw and $ 220 on a chipper. How many of each should be assembled for maximum​ profit?

To attain the maximum​ profit, assemble___ chain saws and ___ wood chippers.

Damon · Answer

profit = 190 s + 220 c
hr = 6 s + 4 c = 48
so 4 c = 48 - 6s
c = 12 - 1.5 s
profit = 190 s + 220 (12 -1.5 s)
profit = 2640 +190 s -330 s = 2640 - 140 s
max when s = 0, make no saws
This makes sense because the chippers make more profit on each and each costs less. 4 c = 48 so make 12 chippers
Are you missing some other constraint?

A chain saw requires 6 hours of assembly and a wood chipper 4 hours. A maximum of 48 hours of assembly time is available. The profit is $ 190 on a chain saw and $ 220 on a chipper. How many of each should be assembled for maximum​ profit?

A chain saw requires 6 hours of assembly and a wood chipper 4 hours. A maximum of 48 hours of assembly time is available. The profit is $ 190 on a chain saw and $ 220 on a chipper. How many of each should be assembled for maximum profit?