How do I find the profit?

Question

y=−44x2+1375x−6548

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.

Answer 1

The profit equation is a parabola. The maximum profit is the vertex of a parabola

y=ax²+bx+c

can be found with the formula:

x = -b/(2a)

For this case:

x = -1375/(2·-44) = 1375/88

x = $15.63