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)=1.2x² - 744x + 126,958. 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)=1.2x² - 744x + 126,958. what is the minimum unit cost? do not round your answer. unit cost: $

Answer

Explanation:

Step1: Identify the coefficients

The cost - function is $C(x)=1.2x^{2}-744x + 126958$, where $a = 1.2$, $b=-744$, $c = 126958$.

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 $x=-\frac{b}{2a}$. $x=-\frac{-744}{2\times1.2}=\frac{744}{2.4}=310$.

Step3: Find the minimum cost

Substitute $x = 310$ into the cost - function $C(x)$. $C(310)=1.2\times(310)^{2}-744\times310 + 126958$. First, calculate $1.2\times(310)^{2}=1.2\times96100 = 115320$. Second, calculate $744\times310=230640$. Then $C(310)=115320-230640 + 126958$. $C(310)=115320+126958-230640$. $C(310)=11828$.

Answer:

$11828$