a company sells widgets. the amount of profit, y, made by the company, is related to the selling price of…

Answer:

$1910$

Explanation:

Step1: Identify the coefficients

For the quadratic function $y = -9x^{2}+501x - 3650$, $a=-9$, $b = 501$, $c=-3650$.

Step2: Find the x - value of the vertex

The x - value of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Substituting the values, we have $x =-\frac{501}{2\times(-9)}=\frac{501}{18}=\frac{167}{6}\approx27.83$.

Step3: Find the maximum profit

Substitute $x = \frac{167}{6}$ into the profit function $y=-9x^{2}+501x - 3650$. [ \begin{align*} y&=-9\times(\frac{167}{6})^{2}+501\times\frac{167}{6}- 3650\ &=-9\times\frac{27889}{36}+\frac{83667}{6}-3650\ &=-\frac{27889}{4}+\frac{83667}{6}-3650\ &=-\frac{83667}{12}+\frac{167334}{12}-\frac{43800}{12}\ &=\frac{-83667 + 167334-43800}{12}\ &=\frac{40067}{12}\approx1910 \end{align*} ]