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?

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