Question

A manufacturer has fixed costs of $16,000 per month and can produce w widgets at a cost of 0.1w^(2) + 20w. How many widgets should be produced monthly to minimize the cost per widget?

Answer 1

Consider c as the cost of the widget so that our given equation is
c = 0.1w^2 + 20w
Take the derivate of the equation.
d/dt (c = 0.1w^2 + 20w)
dc/dt = 0.2w + 20
Given dc/dt = $16000 per month, the number of widgets would contain:
16000 = 0.2w + 20
-0.2w = 20 - 16000
-0.2w = -15980
w = 79900 widgets