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 = -3x² + 249x - 2445

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 = -3x² + 249x - 2445

Answer

Answer:

$41.50$

Explanation:

Step1: Identify the form of the function

The profit function $y = - 3x^{2}+249x - 2445$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-3$, $b = 249$, and $c=-2445$.

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

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 $x=-\frac{b}{2a}$.

Step3: Substitute the values of a and b

Substitute $a=-3$ and $b = 249$ into the formula $x=-\frac{b}{2a}$. We have $x=-\frac{249}{2\times(-3)}$.

Step4: Calculate the value of x

First, calculate the denominator $2\times(-3)=-6$. Then, $x=\frac{249}{6}=41.5$. So the widgets should be sold for $$41.50$ to maximize the profit.