Question

A company sells widgets. The amount of profit, y, made by the company, isrelated to the selling price of each widget, %, by the given equation. Using thisequation, find out the maximum amount of profit the company can make, tothe nearest dollar,y = - 4x^2+ 183x- 1247

Answer 1

Given the equation of the profit:

`y=-4x^2+183x-1247`

To find the maximum profit, we will find the derivative of y

so,

`\begin{gathered} y^(\prime)=-4\cdot2x+183 \\ y^(\prime)=-8x+183=0 \end{gathered}`

solve the equation to find x;

`\begin{gathered} -8x+183=0 \\ -8x=-183 \\ x=(-183)/(-8)=22.875 \end{gathered}`

Substitute with x into the equation of y to find the maximum profit:

`\begin{gathered} y=-4\cdot(22.875)^2+183\cdot22.875-1247 \\ y=845.0625 \end{gathered}`

Rounding to the nearest dollar

so, the answer will be:

The maximum amount of profit the company can make = 845