The total cost (in dollars) for the production of x headphones is: C(x) = 7,000 + 2x

Question

The total cost (in dollars) for the production of x headphones is:

                                        C(x) = 7,000 + 2x

a) Calculate the average cost per unit if 60 headphones are produced

b) Calculate the marginal average cost at a production level of 60 units, and explain the result.                                                                                                 

Answer 1

a) Average cost C(x)/x = 7000/x + 2; at x = 60 C(60)/60 = 7000/60 + 2 = $118.67 per headphone

b)d/dx(C(x)/x) = - 7000/x²; at x = 60 we have - 7000/60² = - $1.94

which means that cost of production of 61st item decreased by $1.94