Each machine at a certain factory can produce 50 units per hour. The setup cost is 45 dollars for each machine and the operating cost is 20 dollars per hour (total, not 20 dollars per machine per hour). You would like to know how many machines should be used to produce 30000 units, with the goal of minimizing production costs.

Question

a) First, find a formula for the total cost in terms of the number of machines, n:

b) The minimum total cost is achieved when using ______ machines for a total cost of _____ dollars.

Answer 1

c = 45n + 20 * 30000/(50n) = 45n + 12000/n
dc/dn = 45 - 12000/n^2
c is minimum when dc/dn = 0

Answer 2

The second and third answers were incorrect. For the second it wants a numerical answer so do I plug in something for n?