This equation represents a parabola. we can find the vertex of this parabola in order to know what's the value to make the maximum profit.
For a equation of the form:
[tex]y=ax^2+bx+c[/tex]
The vertex V(h,k) is given by:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ k=y(h) \end{gathered}[/tex]
for:
[tex]\begin{gathered} y=-5x^2+194x-990 \\ a=-5 \\ b=194 \\ c=-990 \end{gathered}[/tex]
so:
[tex]\begin{gathered} h=\frac{-194}{2(-5)}=19.4 \\ k=y(19.4)=891.8 \end{gathered}[/tex]
Answer:
[tex]19.4_{\text{ }}cents[/tex]
