Question

food truck costs
rena operates a food truck and wants to calculate the balance between costs and revenues.
cost: $c(x) = 5x + 200$
revenue: $r(x) = -x^2 + 50x$
where $x$ represents the number of meals sold.
when does the maximum revenue occur?
the maximum revenue occurs when dropdown meals are sold.
dropdown options: 25, 30, 35, 40

Explanation:

Step1: Identify revenue function type

The revenue function $R(x) = -x^2 + 50x$ is a quadratic function in the form $ax^2+bx+c$ where $a=-1$, $b=50$, $c=0$. Since $a<0$, the parabola opens downward, so its vertex is the maximum point.

Step2: Calculate vertex x-coordinate

For a quadratic $ax^2+bx+c$, the x-coordinate of the vertex is given by $x = -\frac{b}{2a}$.
Substitute $a=-1$, $b=50$:
$x = -\frac{50}{2\times(-1)} = \frac{50}{2} = 25$

Answer:

25