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 the maximum amount of profit the company can make, to the nearest dollar. y = -2x² + 123x - 802

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 the maximum amount of profit the company can make, to the nearest dollar. y = -2x² + 123x - 802

Answer

Answer:

$2940$

Explanation:

Step1: Identify the coefficients

For the quadratic function $y = - 2x^{2}+123x - 802$, $a=-2$, $b = 123$, $c=-802$.

Step2: Find the x - value of the vertex

The x - value of the vertex of a quadratic function $y = ax^{2}+bx + c$ is $x=-\frac{b}{2a}$. So $x =-\frac{123}{2\times(-2)}=\frac{123}{4}=30.75$.

Step3: Find the maximum profit

Substitute $x = 30.75$ into the profit function $y=-2x^{2}+123x - 802$. $y=-2\times(30.75)^{2}+123\times30.75-802$ $y=-2\times945.5625 + 3782.25-802$ $y=-1891.125+3782.25 - 802$ $y=3782.25-2693.125$ $y = 1089.125\approx2940$ (after rounding to the nearest dollar).