Question

A manufacturer of turds finds that for the first 500 units of turds that are produced and sold, the profit is 70 dollars per turd. The profit on each of the turds beyond 500 is decreased by 0.10 times the number of additional units sold. What level of output will maximize the profit?

Answer 1

define profit function :
for x<500
P(x) = 70x
for x>500
P(x) = (70*500) + (70-.1(x-500))(x-500) = 35,000 +70(x-500) -.1(x-500)^2

maximize profit when P'(x) = 0
P'(x) = 70 -.2(x-500) = 0
70 = .2(x-500)
170 = .2x
850 = x

producing 850 units maximizes profit

Answer 2

THANK YOU SO MUCH!!

Answer 3

welcome