question\na company sells widgets. the amount of profit, y, made by the company, is related to the selling…

question\na 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$y=-x^{2}+82x - 548$

question\na 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$y=-x^{2}+82x - 548$

Answer

Explanation:

Step1: Identify the form of the function

The profit function $y = -x^{2}+82x - 548$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-1$, $b = 82$, $c=-548$.

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

For a quadratic function $y = ax^{2}+bx + c$, the x - coordinate of the vertex (which gives the value of $x$ for maximum or minimum of the function) is $x=-\frac{b}{2a}$. Substitute $a=-1$ and $b = 82$ into the formula: $x=-\frac{82}{2\times(-1)}$

Step3: Calculate the value of x

$x = \frac{82}{2}=41$

Answer:

$41.00$