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)=0.1x^2-40x+9569. How many machines must be made to minimize the unit cost?
Do not round your answer.

Answer 1

Answer:

200

Step-by-step explanation:

Given that C(x) = 0.1$x^{2}$ - 40x +9569,

complete the square, then C(x) = 0.1* ( $x^{2}$ - 400x) +9569

                                                    = 0.1 * ($x^{2}$ - 400x + $(400/2)^{2}$) +9569 - $(400/2)^{2}$

                                                    = 0.1 * (x - 200)^2 - 30431

so the answer is 200 machines