Question

How would u do this w/o plugging in numbers? Thanks for your time and help!

Answer 1

If you know calculus, you can take the derivative and find the critical point.

The simpler method would be to complete the square. We have

$R=-\dfrac1{800}(x^2-2400x)=-\dfrac1{800}(x^2-2400x+1200^2-1200^2)$
$R=-\dfrac1{800}\left((x-1200)^2-1200^2\right)=-\dfrac1{800}(x-1200)^2+\dfrac{1200^2}{800}$

The first term will always be negative, so whenever it vanishes, we're left with the maximum value at $\dfrac{1200^2}{800}=1800$, so the answer is C.