Question

the total cost of producing a type of truck is given by $c(x)=25000 - 80x + 0.1x^{2}$, where $x$ is the number of trucks produced. how many trucks should be produced to incur minimum cost? answer how to enter your answer (opens in new window)

Explanation:

Step1: Identify the function type

The cost function $C(x)=25000 - 80x+0.1x^{2}$ is a quadratic function in the form of $y = ax^{2}+bx + c$, where $a = 0.1$, $b=-80$ and $c = 25000$.

Step2: Use the formula for the vertex of a quadratic

For a quadratic function $y = ax^{2}+bx + c$, the x - coordinate of the vertex (which gives the minimum value when $a>0$) is $x=-\frac{b}{2a}$.
Substitute $a = 0.1$ and $b=-80$ into the formula:
$x=-\frac{-80}{2\times0.1}$.

Step3: Calculate the value of x

First, simplify the denominator: $2\times0.1 = 0.2$.
Then, $x=\frac{80}{0.2}=400$.

Answer:

400