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 = -x² + 103x - 980

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 = -x² + 103x - 980

Answer

Explanation:

Step1: Identify the function type

The profit function $y = -x^{2}+103x - 980$ is a quadratic function in the form $y = ax^{2}+bx + c$ where $a=-1$, $b = 103$, $c=-980$.

Step2: Recall the vertex - formula

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

Step3: Calculate the value of $x$

Substitute $a=-1$ and $b = 103$ into the formula $x=-\frac{b}{2a}$. $x=-\frac{103}{2\times(-1)}=\frac{103}{2}=51.5$

Answer:

$51.50$