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.\n\n$y = -5x^{2}+209x - 1090$

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.\n\n$y = -5x^{2}+209x - 1090$

Answer

Explanation:

Step1: Identify the coefficients

For the quadratic function $y = ax^{2}+bx + c$, here $a=-5$, $b = 209$, $c=-1090$.

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

The x - value of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Substitute $a=-5$ and $b = 209$ into the formula: $x=-\frac{209}{2\times(-5)}=\frac{209}{10}=20.9$

Answer:

$$20.90$