A large hotel finds that it can rent 95 rooms when it charge $100 per room. For each $1 increase in room cost it rents one room less. (Likewise, for each $1 decrease in room cost it rents one room more)

Question

What price should it charge in order to maximize the revenue?

Answer 1

if there are x price increases, the revenue is

(95-x)(100+x)

That is just a parabola. Its vertex represents maximum revenue.