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 $c(x)=0.5x^2 - 280x + 58,665$. what is the minimum unit cost?
do not round your answer.

Explanation:

Step1: Find vertex x-coordinate

For quadratic $ax^2+bx+c$, $x=-\frac{b}{2a}$. Here $a=0.5$, $b=-280$.
$x=-\frac{-280}{2\times0.5}=\frac{280}{1}=280$

Step2: Substitute x into cost function

Calculate $C(280)=0.5(280)^2 -280(280)+58665$
First term: $0.5\times78400=39200$
Second term: $-280\times280=-78400$
Sum: $39200 -78400 +58665 = (39200+58665)-78400=97865-78400=19465$

Answer:

19465