The problem asks to find the maximum revenue for the revenue function $R(x) = 358x - 0.9x^2$. The answer should be rounded to the nearest cent.

1. Problem Description

The problem asks to find the maximum revenue for the revenue function $R(x) = 358x - 0.9x^2$. The answer should be rounded to the nearest cent.

2. Solution Steps

To find the maximum revenue, we need to find the vertex of the quadratic function $R(x) = 358x - 0.9x^2$. This is a quadratic function in the form of $R(x) = ax^2 + bx + c$, where $a = -0.9$, $b = 358$, and $c = 0$. Since $a < 0$, the parabola opens downward, so the vertex represents the maximum value of the function.

The x-coordinate of the vertex is given by the formula:

$x = -\frac{b}{2a}$

Substituting the values of $a$ and $b$, we get:

$x = -\frac{358}{2(-0.9)} = -\frac{358}{-1.8} = \frac{358}{1.8} \approx 198.8889$

Now, substitute this value of $x$ back into the revenue function $R(x)$ to find the maximum revenue:

$R(198.8889) = 358(198.8889) - 0.9(198.8889)^2$

$R(198.8889) = 71202.2222 - 0.9(39556.8765)$

$R(198.8889) = 71202.2222 - 35601.1889$

$R(198.8889) = 35601.0333$

Rounding to the nearest cent, we get $35601.03$.

3. Final Answer

$35601.03