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) = 0.6x² - 420x + 89,377. how many machines must be made to minimize the unit cost? do not round your answer. number of copy machines:

Explanation:

Step1: Identify the function type

The cost function \(C(x) = 0.6x^{2}-420x + 89377\) is a quadratic function in the form \(y = ax^{2}+bx + c\), where \(a = 0.6\), \(b=-420\), \(c = 89377\).

Step2: Use the formula for the vertex of a quadratic function

For a quadratic function \(y = ax^{2}+bx + c\), the \(x\)-coordinate of the vertex (which gives the minimum for \(a>0\)) is \(x=-\frac{b}{2a}\).
Substitute \(a = 0.6\) and \(b=-420\) into the formula:

$$x=-\frac{-420}{2\times0.6}$$

$$x=\frac{420}{1.2}$$

$$x = 350$$

Answer:

\(350\)