a supply company manufactures copy - machines. the unit cost c (the cost in dollars to make each copy…

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)=0.3x² - 108x + 23410. how many machines must be made to minimize the unit cost? do not round your answer. number of copy machines:

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)=0.3x² - 108x + 23410. how many machines must be made to minimize the unit cost? do not round your answer. number of copy machines:

Answer

Explanation:

Step1: Identify the function type

The cost function $C(x)=0.3x^{2}-108x + 23410$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a = 0.3$, $b=-108$, and $c = 23410$.

Step2: Recall the vertex - formula for a quadratic function

For a quadratic function $y = ax^{2}+bx + c$, the x - coordinate of the vertex (which gives the minimum value when $a>0$) is $x=-\frac{b}{2a}$.

Step3: Calculate the value of x

Substitute $a = 0.3$ and $b=-108$ into the formula $x=-\frac{b}{2a}$. $x=-\frac{- 108}{2\times0.3}=\frac{108}{0.6}=180$.

Answer:

180