# Calculus/economics? Find maximum profit, average cost per unit?

A given commodity has a demand function given by p = 100 - 0.5x^2 and a total cost function of C = 4x + 375.
a. What price gives the maximum profit?
b. What is the average cost per unit if production is set to give maximum profit?
I did part a, stuck on part b.
my work for a:
P = -0.5x^3 + 96x -...
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A given commodity has a demand function given by p = 100 - 0.5x^2 and a total cost function of C = 4x + 375.

a. What price gives the maximum profit?

b. What is the average cost per unit if production is set to give maximum profit?

I did part a, stuck on part b.

my work for a:

P = -0.5x^3 + 96x - 375

P' = -3/2x^2 + 96 = 0

x = 8

p = 100 - 0.5(8)^2 = 68

Answer for a: $68 will give maximum profit

The answer in the back verifies this as answer, answer to part b is $50.88, could someone help guide me in the right direction or set it up so I could solve it?

a. What price gives the maximum profit?

b. What is the average cost per unit if production is set to give maximum profit?

I did part a, stuck on part b.

my work for a:

P = -0.5x^3 + 96x - 375

P' = -3/2x^2 + 96 = 0

x = 8

p = 100 - 0.5(8)^2 = 68

Answer for a: $68 will give maximum profit

The answer in the back verifies this as answer, answer to part b is $50.88, could someone help guide me in the right direction or set it up so I could solve it?

Update:
Aah I feel so silly, thank you so much guys, it was just a matter of plugging back in value, I overthought it and thought it to be more complicated, haha thanks so much.

Update 2:
Aah I feel so silly, thank you so much guys, it was just a matter of plugging back in value, I overthought it and thought it to be more complicated, haha thanks so much.

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