a medical equipment industry manufactures x - ray machines. the unit cost c (the cost in dollars to make…

a medical equipment industry manufactures x - ray machines. the unit cost c (the cost in dollars to make each x - ray machine) depends on the number of machines made. if x machines are made, then the unit cost is given by the function c(x)=1.2x² - 504x + 71,791. what is the minimum unit cost? do not round your answer. unit cost: $

a medical equipment industry manufactures x - ray machines. the unit cost c (the cost in dollars to make each x - ray machine) depends on the number of machines made. if x machines are made, then the unit cost is given by the function c(x)=1.2x² - 504x + 71,791. what is the minimum unit cost? do not round your answer. unit cost: $

Answer

Explanation:

Step1: Identify the coefficients

The cost function is $C(x)=1.2x^{2}-504x + 71791$, where $a = 1.2$, $b=-504$, $c = 71791$.

Step2: Find the x - value of the vertex

The x - value of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. So, $x=-\frac{-504}{2\times1.2}=\frac{504}{2.4}=210$.

Step3: Find the minimum cost

Substitute $x = 210$ into the cost function $C(x)$. $C(210)=1.2\times(210)^{2}-504\times210 + 71791$. First, calculate $1.2\times(210)^{2}=1.2\times44100 = 52920$. Second, calculate $504\times210 = 105840$. Then $C(210)=52920-105840 + 71791$. $C(210)=52920+71791-105840=124711 - 105840=18871$.

Answer:

$18871$