Answer
$23$ computers
$\$16,900$
Work Step by Step
The quadratic function
$$f(x)=-x^2+46x-360$$
has negative leading coefficient, therefore its graph is a parabola that opens downward and has a maximum in the vertex.
Bring the function to the vertex form $f(x)=a(x-h)^2+k$:
$$\begin{align*}
f(x)&=-x^2+46x-360\\
&=-(x^2-46x)-360\\
&=-(x^2-46x+23^2)+23^2-360\\
&=-(x-23)^2+169.
\end{align*}$$
Identify the constants $a$, $h$, $k$:
$$\begin{align*}
a&=-1\\
h&=23\\
k&=169.
\end{align*}$$
Determine the vertex of the function:
$$(h,k)=(23,169).$$
So the number of computers that should be manufactured each day is $23$, while the maximum daily profit is $\$16,900$.
