A commodity has a demand function modeled by p = 104 − 0.5x and a total cost function modeled by C = 30x + 35.75, where x is the number of units.

Question

(a) What price yields a maximum profit? $ per unit?

(b) When the profit is maximized,what is the average cost per unit? (Round answer to two decimal places)

Answer 1

Revenue = x * demand

x(104 - 0.5x) - 30x - 35.75 = Profit(x) is the profit function

=104x - 0.5x^2 - 30x - 35.75

= - 0.5x^2 + 74x - 35.75

0 = dP/dx = -x + 74

x=74