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=-\frac1{800}(x^2-2400x)=-\frac1{800}(x^2-2400x+1200^2-1200^2)`

`R=-\frac1{800}\left((x-1200)^2-1200^2\right)=-\frac1{800}(x-1200)^2+(1200^2)/(800)`

The first term will always be negative, so whenever it vanishes, we're left with the maximum value at
`(1200^2)/(800)=1800`, so the answer is C.