Question

Click here to view the transcript The net profit in dollars per day for a small business owner is given by the equation f (x) = -0.1.r2 + 6.r + 5, where x is the number of employees he hires. If he hires the number of employees that will maximize his profit, what will his profit be in dollars per day? (Enter an exact number.) X dollars per day Need Help? Read It Show My Work (Optional) Submit Answer Type here to search O 8:37 PM 3/20/2021

Answer 1

Given the function:

`f(x)=-0.1x^2+6x+5`

Where f is the profit and x is the number of employees he hires

For maximum profit: df/dx = 0

so,

`\begin{gathered} (df)/(dx)=-0.1\cdot2x+6 \\ (df)/(dx)=-0.2x+6=0 \end{gathered}`

solve for x

`\begin{gathered} -0.2x+6=0 \\ -0.2x=-6 \\ \\ x=(-6)/(-0.2)=30 \end{gathered}`

So, the maximum profit will be at x = 30

The profit will be :

`f(30)=-0.1\cdot30^2+6\cdot30+5=95`

so, the answer will be:

His profit per day = $95