Given the function:
[tex]f(x)=-0.1x^2+6x+5[/tex]Where f is the profit and x is the number of employees he hires
For maximum profit: df/dx = 0
so,
[tex]\begin{gathered} \frac{df}{dx}=-0.1\cdot2x+6 \\ \frac{df}{dx}=-0.2x+6=0 \end{gathered}[/tex]solve for x
[tex]\begin{gathered} -0.2x+6=0 \\ -0.2x=-6 \\ \\ x=\frac{-6}{-0.2}=30 \end{gathered}[/tex]So, the maximum profit will be at x = 30
The profit will be :
[tex]f(30)=-0.1\cdot30^2+6\cdot30+5=95[/tex]so, the answer will be:
His profit per day = $95
