The profit function for a certain commodity is P(x) = 120x - x2 - 1000. Find the level of production that yields maximum profit, and find the maximum profit.

Question

x= ? units

 

p= $          ?

Answer 1

P(x)=120x-x²-1000

0=-x²+120x-1000

use -b/2a or take the first derivative

-b/2a=-120/-2=60 units for x

taking the first derivative...

0=-2x+120

2x=120

x=60 again

maximum profit is -(60)²+(120)(60)-1000=-3600+7200-1000=7200-4600=$2600.00