Question

The cost of manufacturing x items is given by C(x) = 0.02x^2 + 20x + 1800. Find the marginal cost function. Compuare the marginal cost at x = 20 to the actual cost of producing the 20th item.

Answer 1

This is what I did but my teacher said its wrong

C(x) = 0.02x^2 + 20x + 1800
C’(x) = 0.04x + 20
C’(20) = 0.04(20) + 20 = 20.8 so this will be the marginal cost at x = 20
Acutal cost of the 20th item : c(20) - c(19) = 0.02(20^2) + 20(20) + 1800 – 0.02(19)^2 + 20(19) + 1800 = 4380.78

Answer 2

there is a lot of difference between marginal and actual cost.