Given the equation of the profit:
[tex]y=-4x^2+183x-1247[/tex]To find the maximum profit, we will find the derivative of y
so,
[tex]\begin{gathered} y^{\prime}=-4\cdot2x+183 \\ y^{\prime}=-8x+183=0 \end{gathered}[/tex]solve the equation to find x;
[tex]\begin{gathered} -8x+183=0 \\ -8x=-183 \\ x=\frac{-183}{-8}=22.875 \end{gathered}[/tex]Substitute with x into the equation of y to find the maximum profit:
[tex]\begin{gathered} y=-4\cdot(22.875)^2+183\cdot22.875-1247 \\ y=845.0625 \end{gathered}[/tex]Rounding to the nearest dollar
so, the answer will be:
The maximum amount of profit the company can make = 845
