a company sells widgets. the amount of profit...
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).