Calculus: Cost of Production

Question

Consider the cost function C(x)= 32400 + 300x+x^2 dollars, where x denotes the production level of widgets.

a.) The cost of production level 1300 ____ dollars.

b.) The average cost at the production level 1300 _____ dollars/widget.

c.) The production level that will minimize the average cost _____ widgets.

d.) The minimal average cost is ____ dollars/widget.

Answer 1

a.) C(1300) = 32400 + 300·1300 + 1300² = $2112400

b.) C(1300)/1300 = $1624.92 per widget

c) (C(x)/x)' = d/dx(32400/x + 300 + x) = - 32400/x² + 1 = 0; x = √32400 = 180 widgets.

C''(x) = 62800/x³; C''(180) = 62800/180³ = 1/90 > 0. So, by 2nd derivative test we have min

d.) min(C(x)/x) = C (180)/180 = $660 per widget