Answer to Question #174438 in Calculus for Jc Young

Question

The cost in dollars of producing x headphones is C(x)= 1600+100x-0.1x²

a) calculate average cost of producing 200 headphones

b) calculate the marginal cost of producing the 200th headphone

Answer 1

a). We allow for the number of headphones to take positive real values. The mean value (average cost) is: $\mu=\frac{C(x)}{x}=\frac{1600}{x}+1000-0.1x$. We subsitute $x=200$ and get: $\mu=8+1000-20=988$

b). The marginal cost is given by formula $C'(x)=100-0.2x$. For $x=200$ we receive: $C(200)=60$