Find the marginal cost

Question

Suppose that the total cost in dollars of producing x units of a product is given by

C(x) = 5,000 + 30xe^x/800.

Find the marginal cost when 800 units are produced. (Round your answer to the nearest cent.)

Answer 1

Marginal cost is given by the first derivative of the total cost function with respect to quantity, which is:

C^'(x) = 30 e^x/800 + (30 x e^x/800)/800. Plugging in x=800 in this we obtain marginal cost of 163.09.