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 = -9x^2 + 700x - 6005

Answer 1

Answer:

Widgets should be sold by $38.88 to maximize the profit.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

$f(x) = ax^{2} + bx + c$

It's vertex is the point $(x_{v}, y_{v})$

In which

$x_{v} = -\frac{b}{2a}$

$y_{v} = -\frac{\Delta}{4a}$

Where

$\Delta = b^2-4ac$

If a<0, the vertex is a maximum point, that is, the maximum value happens at $x_{v}$, and it's value is $y_{v}$.

In this question:

The profit is given by:

$y = -9x^2 + 700x - 6005$

Which is a quadratic function with $a = -9, b = 700, c = -6005$

The maximum profit happens at the x of the vertex. Thus

$x_{v} = -\frac{b}{2a} = -\frac{700}{2(-9)} = 38.88$

Widgets should be sold by $38.88 to maximize the profit.