What is the minimum unit cost?. Do not round your answer.

Question

A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function: C(x) = 0.8x² - 352x + 58,583 . 

Answer 1

take the derivative, set it equal to zero, solve for x

C' = 1.6x - 352 = 0

x = 352/1.6 = 220

C(220) = 0.8(220)^2 -352(220) + 58583 = 38720 - 77440 + 58583 = 19863