Question

handmade candles
april sells handmade candles at a local market and wants to analyze the business’s financial situation.
cost: $c(x) = 3x + 50$
revenue: $r(x) = -x^2 + 30x$
when does maximum revenue occur?
the maximum revenue occurs when you sell candles.
(options: 2, 15, 125, 225)

Explanation:

Step1: Identify revenue function type

The revenue function $R(x) = -x^2 + 30x$ is a quadratic function in the form $ax^2+bx+c$, where $a=-1$, $b=30$, $c=0$. 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 $x = -\frac{b}{2a}$.
Substitute $a=-1$, $b=30$:
$x = -\frac{30}{2(-1)} = \frac{30}{2} = 15$

Answer:

15