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

200

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