Suppose that the total cost in dollars of producing x units of a product is given by C(x) = 10,000 + 30xex/500. Find the marginal cost when 500 units are produced.

Question

Suppose that the total cost in dollars of producing x units of a product is given by C(x) = 10,000 + 30xex/500. Find the marginal cost when 500 units are produced. 

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

C(x) = 10,000 + 30xe^x/500. 

Find the marginal cost when 500 units are produced. (Round your answer to the nearest cent.) 

Answer 1

C(x) = 10000 + 30xe^x/500;

Marginal cost C'(x) = 30e^x/500 + 30/500xe^x/500 = e^x/500(30 + 3x/50);

C'(500) = e(30 + 30) = 60e = $163 per unit