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)=0.8x² - 176x + 24,265. 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)=0.8x² - 176x + 24,265. what is the minimum unit cost? do not round your answer. unit cost: $

Answer

Explanation:

Step1: Identify the function type

The cost function $C(x)=0.8x^{2}-176x + 24265$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a = 0.8$, $b=-176$, and $c = 24265$.

Step2: Find the x - value of the vertex

The x - coordinate of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Substitute $a = 0.8$ and $b=-176$ into the formula: $x=-\frac{-176}{2\times0.8}=\frac{176}{1.6}=110$.

Step3: Find the minimum cost

Substitute $x = 110$ into the cost function $C(x)$: $C(110)=0.8\times(110)^{2}-176\times110 + 24265$. First, calculate $0.8\times(110)^{2}=0.8\times12100 = 9680$. Second, calculate $176\times110 = 19360$. Then $C(110)=9680-19360 + 24265$. $C(110)=9680+24265-19360=14585$.

Answer:

$14585$