Question

Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is C(x) = 2500 + 2x + 0.03x² + 0.0002x³. Find C'(60).

Answer 1

To find the marginal cost of producing 60 pairs of jeans, take the derivative of the cost function and substitute x = 60.

Step-by-step explanation:

To find C'(60), which represents the marginal cost of producing 60 pairs of jeans, we need to take the derivative of the cost function C(x). Taking the derivative of each term, we get:

C'(x) = 2 + 0.06x + 0.0006x²

Substituting x = 60 into the derivative formula, we can calculate C'(60):

C'(60) = 2 + 0.06(60) + 0.0006(60²)

C'(60) = 2 + 3.6 + 2.16 = 7.76

Therefore, the marginal cost of producing 60 pairs of jeans is $7.76.