Question

A company sells widgets. The amount ofprofit, y, made by the company, is related tothe selling price of each widget, x, by thegiven equation. Using this equation, findout what price the widgets should be soldfor, to the nearest cent, for the company tomake the maximum profit.

Answer 1

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:

$y=ax^2+bx+c$

The vertex V(h,k) is given by:

$\begin{gathered} h=\frac{-b}{2a} \\ k=y(h) \end{gathered}$

for:

$\begin{gathered} y=-5x^2+194x-990 \\ a=-5 \\ b=194 \\ c=-990 \end{gathered}$

so:

$\begin{gathered} h=\frac{-194}{2(-5)}=19.4 \\ k=y(19.4)=891.8 \end{gathered}$

Answer:

$19.4_{\text{ }}cents$