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 + 30xe^x/500. 

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

Answer 1

take the derivative and plug in x = 500

C'(x) = 30xe^x/500 + 30e^x/500

C'(x) = 30(500)e + 30e = 15030e = about $41,061.96 = Marginal Cost when x = 500