Answer
$100$ units for $4000$ dollars.
Work Step by Step
First, let rewrite the function so that the terms are in the usual order:
$R(x)=-0.4x^2+80x$
In this quadratic function, $a=-0.4$, $b=80$ and $c=0$. With this information known, we can find when the maximum value occurs, as well as the maximum value of the function:
The maximum value occurs at:
$x=\frac{-b}{2a}=\frac{-80}{-0.8}=100$
Therefore, the maximum value is:
$R(100)=-0.4*100^2+80*100=-0.4*10000+8000=-4000+8000=4000$
In conclusion, the maximum revenue is $4000$ dollars, and they need to manufacture $100$ units to harness that revenue.
