Question

The net profit in dollars per day for a small business owner is given by the equation f(x) = -0.1x^2 + 6 x + 4, 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.) dollars per day

Answer 1

Answer:

$\large \boxed{\sf \ \ \text{The maximum profit is \ 94 per day.} \ \ }$

Step-by-step explanation:

Hello,

The coefficient in $x^2$ is negative.

So, there is a maximum at the vertex point which is

$x=-\dfrac{b}{2a}==\dfrac{-6}{-0.2}=\dfrac{6}{0.2}=30$

And then the maximum is f(30)=

$-0.1\cdot 30^2+6\cdot 30 +4=-90 +180+4=94$

So the maximum profit is 94 $ per day.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you