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

Explanation:

Step1: Identify coefficients

For the quadratic function $y = - 49x^{2}+1875x - 10599$, $a=-49$, $b = 1875$, $c=-10599$.

Step2: Find x - coordinate of vertex

The x - coordinate of the vertex of a quadratic function $y = ax^{2}+bx + c$ is $x=-\frac{b}{2a}$. So $x =-\frac{1875}{2\times(-49)}=\frac{1875}{98}\approx19.13$.

Step3: Find y - coordinate of vertex

Substitute $x=\frac{1875}{98}$ into the function $y=-49x^{2}+1875x - 10599$. $y=-49\times(\frac{1875}{98})^{2}+1875\times\frac{1875}{98}-10599$ $y=-49\times\frac{1875^{2}}{98^{2}}+\frac{1875^{2}}{98}-10599$ $y=\frac{-49\times1875^{2}+98\times1875^{2}}{98^{2}}-10599$ $y=\frac{49\times1875^{2}}{98^{2}}-10599$ $y=\frac{1875^{2}}{196}-10599$ $y=\frac{3515625}{196}-10599$ $y=\frac{3515625 - 10599\times196}{196}$ $y=\frac{3515625-2077404}{196}$ $y=\frac{1438221}{196}\approx7338$.

Answer:

$7338$