Answer to Question #172681 in Calculus for Todd Phillips

Question

The cost in dollars of producing x headphones is

C(x) = 2000 + 150x – 0.1x²

a. Calculate the average cost of producing 250 headphones.

b. Calculate the marginal cost of producing the 250th headphone. 

Answer 1

$a) C(x) = 2000+150x-0.1x^2\\ C(250) = 2000+150(250)-0.1(250)^2 = 2000+37500-6250=33250\\$

Average cost of x quantity = $\frac{C(x)}{x}$

So average cost of 250 headphones = $\frac{C(250)}{250} = \frac{33250}{250} = 133$

i.e The average cost of producing 250 headphones is 133 dollars.

b) Let M denote marginal cost.

We have that $M = \dfrac{dC(x)}{dx} = 150-0.2x$

$\therefore M(250) = 150-0.2(250) = 150- 50 = 100$

i.e The marginal cost of producing the 250th headphone is 100 dollars.