Question

Cost function=400Q-50Q^2+5Q^3

What is the level of output at which the production of the uniform minimize the company's ATC

Answer 1

$TC = 400Q-500Q^2+5Q^3$

$ATC =\frac{TC}{Q}=400-500Q+5Q^2$

$\text{find min ATC:}$

$ATC'=(400-500Q+5Q^2)'=-500+10Q$

$ATC'=0;-500+10Q=0;Q=50$

$ATC'(49)=-500+490=-10<0$

$ATC'(51)=-500+510=10>0$

$\text{hence } Q=50 \text{minimum point of function }ATC$

$\text{Answer: }50$