Question

The cost C of building a house is related to the number k of carpenters used and the number e of electricians used by

C(k, e) = 15,000 + 30k2 + 60e2.
If six electricians are currently employed in building your new house and the marginal cost per additional electrician is the same as the marginal cost per additional carpenter, how many carpenters are being used? (Round your answer to the nearest carpenter.)

Answer 1

k = number of carpenters = 10
C = 15,000+50(10)^2 +60x^2
C = 15,000+5,000+60x^2
C = 20,000+60x^2 ----- cost function

Marginal cost function = dC/dx = d/dx [60x^2] = 120x
MC = 120x ----- marginal cost function

Average cost function = C(x)/x = 20,000 /x + 60x
AC = 20,000/x + 60x

Marginal cost when x=14 is:
120(14) = 1,680

Average cost when x=14 is:
20,000/14 + 60(14) = 2268.57

Marginal cost is less than the average cost, so the average cost is decreasing as the number of electricians increases.