a vehicle factory manufactures cars. the unit cost c (the cost in dollars to make each car) depends on the…

a vehicle factory manufactures cars. the unit cost c (the cost in dollars to make each car) depends on the number of cars made. if x cars are made, then the unit cost is given by the function c(x)=0.2x² - 36x + 18,689. what is the minimum unit cost? do not round your answer. unit cost: $

a vehicle factory manufactures cars. the unit cost c (the cost in dollars to make each car) depends on the number of cars made. if x cars are made, then the unit cost is given by the function c(x)=0.2x² - 36x + 18,689. what is the minimum unit cost? do not round your answer. unit cost: $

Answer

Explanation:

Step1: Identify the function type

The function $C(x)=0.2x^{2}-36x + 18689$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a = 0.2$, $b=-36$, and $c = 18689$.

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 $a = 0.2$ and $b=-36$ into the formula: $x=-\frac{-36}{2\times0.2}=\frac{36}{0.4}=90$.

Step3: Find the minimum cost

Substitute $x = 90$ into the cost function $C(x)$: $C(90)=0.2\times(90)^{2}-36\times90 + 18689$. First, calculate $0.2\times(90)^{2}=0.2\times8100 = 1620$. Second, calculate $36\times90=3240$. Then $C(90)=1620-3240 + 18689$. $C(90)=17069$.

Answer:

$17069$