Really confused on this: "An electric scooter manufacturer...."

Question

An electric scooter manufacturer estimates that the cost C in dollars) of producing x scooters is given by C(x) = 600+ 0.05x + 0.0002x². Find the production level, to the nearest unit, that will minimize the average cost Č(x) per unit.

Answer 1

Average Cost = total cost divided by production level

AC = C/x = 600/x +0.05 + 0.0004x

take the derivative and set = 0

(AC)' = -600/x^2 + 0.0004 = 0

600/x^2 = 0.0004

0.0004x^2 = 600

x^2 = 600/0.0004 = 1500000

x = sqr1500000 =1224.7

1225 is the production level that minimizes average cost