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 $c(x)=0.4x^2 - 272x + 52,904$. how many machines must be made to minimize the unit cost? do not round your answer. number of copy machines:

Explanation:

Step1: Identify quadratic form

The function is $C(x)=0.4x^2 - 272x + 52904$, a quadratic $ax^2+bx+c$ with $a>0$, so it opens upward, and the vertex is the minimum.

Step2: Use vertex x-coordinate formula

For $ax^2+bx+c$, vertex x-value is $x=-\frac{b}{2a}$. Here $a=0.4$, $b=-272$.
<Expression>
$x=-\frac{-272}{2\times0.4}$
</Expression>

Step3: Calculate the value

Simplify the expression to find x.
<Expression>
$x=\frac{272}{0.8}=340$
</Expression>

Answer:

340