Suppose a company has estimated that the marginal cost of manufacturing x items is $c ^ { \prime } ( x ) = 5 + 0.02 x$ (measured in dollars per unit) with a fixed start-up cost of c(0) = 10,000. Find the cost of producing the first 500 items.
A)$15,000
B)$5,000
C)$10,000
D)$17,500
E)$25,000
F)$6000
G)$20,000
H)$60,000

Question

Quizplus · Accepted Answer

The cost of producing the first 500 items is the integral of the marginal cost function from 0 to 500:$$\int_0^{500} (5 + 0.02x) dx = [5x + 0.01x^2]_0^{500} = 5(500) + 0.01(500)^2 - 0 = 15,000$$

Suppose a Company Has Estimated That the Marginal Cost of Manufacturing