Question

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

      C (k,e) = 15,000 + 50k²+ 60e²

If three 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

Marginal Cost per additional electrician(MC_e) is given by:

Here it is given that e = number of electricians = 3

=> MC_e = 120*3 = 360

Marginal Cost per additional carpenter(MC_k) is given by:

=> MC_k = 100k

As it is given that,  the marginal cost per additional electrician is the same as the marginal cost per additional carpenter

=> MC_k = MC_e

=> 100k = 360

=> k = 3.6 ~ 4 carpenter(Approx after rounding)

=> Number of carpenter used = 4 carpenter