A company's revenue is modeled by R(x) = -5x² + 200x, where x is the number of items sold in hundreds. How many hundreds of items should…

Revenue is a downward-opening parabola, so its maximum is at the vertex: $x=-\frac{b}{2a}=-\frac{200}{2(-5)}=\frac{-200}{-10}=20$ hundred items, choice G. The maximum revenue is $R(20)=-5(400)+200(20)=-2000+4000=2000$. Choice F ($10$) is half the correct value, where $R=1500$. Choice H ($40$) doubles it, where $R=0$ ($-8000+8000$), which is the other zero of the revenue function. Choice J ($100$) gives a large negative revenue. The vertex lies exactly halfway between the zeros $x=0$ and $x=40$. Reread the question to make sure the answer is in hundreds of items, not items.