Question

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.

y=-15x^2+801x-5900

Answer 1

In order to maximize profit, each widget should sell for $26.70.

Explanation:

The total amount of profit y given by the selling price of each widget x is given by:

And we want to determine the price of each widget such that is yields the maximum profit.

Since the equation is a quadratic, the maximum profit will occur at the vertex of our parabola.

The vertex of a quadratic is given by:

So, let's find the vertex. In our equation, a = -15, b = 801, and c = -5900.

Therefore, the price that maximizes profit is:

Therefore, in order to maximize profit, each widget should sell for $26.70.

Notes:

Then substituting this back into the equation, the maximum profit is: