a company sells widgets. the amount of profit, y, made by the company, is related to the selling price of…

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 = -5x² + 286x - 2275

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 = -5x² + 286x - 2275

Answer

Explanation:

Step1: Identify the coefficients

The profit - function is a quadratic function $y = ax^{2}+bx + c$, where $a=-5$, $b = 286$, and $c=-2275$.

Step2: Use the formula for the x - coordinate of the vertex

The x - coordinate of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Substitute $a=-5$ and $b = 286$ into the formula: $x=-\frac{286}{2\times(-5)}=\frac{286}{10}=28.6$

Answer:

$$28.60$