Question

A company sells widgets. The amount of profit, y, made by the company, is related tothe selling price of each widget, x, by the given equation. Using this equation, find outthe maximum amount of profit the company can make, to the nearest dollar.y = -29x² + 13880 - 10040

Answer 1

`\begin{gathered} y=-29x^2+13880x-10040 \\ \text{For maxi}mum\text{ profit,} \\ (dy)/(dx)=0 \\ (d(-29x^2+13880x-10040))/(dx)=0 \\ -58x+13880=0 \\ x=(13880)/(58) \\ x=239.3 \\ \text{Now, profit is,} \\ \text{Profit}=-29(239.3)^2+13880(239.3)-10040 \\ \text{Profit}=\text{ \$1650774} \end{gathered}`