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 = -6x² + 319x - 2460

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 = -6x² + 319x - 2460

Answer

Explanation:

Step1: Identify the coefficients

The profit - function is a quadratic function $y = ax^{2}+bx + c$, where $a=-6$, $b = 319$, and $c=-2460$. For a quadratic function $y = ax^{2}+bx + c$, the x - value of the vertex (which gives the maximum or minimum of the function) is given by $x=-\frac{b}{2a}$.

Step2: Calculate the x - value of the vertex

Substitute $a=-6$ and $b = 319$ into the formula $x=-\frac{b}{2a}$. $x=-\frac{319}{2\times(-6)}=\frac{319}{12}\approx26.5833$.

Step3: Round to the nearest cent

Rounding $\frac{319}{12}\approx26.5833$ to the nearest cent gives $x = 26.58$.

Answer:

$26.58$