so.. check the picture below
that's when the profit gets maximized
[tex]\bf \qquad \textit{vertex of a parabola}\\ \quad \\
\begin{array}{lccclll}
P(x)=&-0.002x^2&+5.5x&-1000\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]
how many items does the company need to sell? they need to sell [tex]\bf -\cfrac{{{ b}}}{2{{ a}}}[/tex]
