Thread: optimization

A 150 room hotel will rent all of its room if it charges $40 per room. The manager knows that for each $2 dollar increase per room, eight fewer room will be rented per night. What rent would maximize the revenue per night?

I'm having trouble setting up the equation.
I said w= each $2 dollar increase
so revenue= (150-8w)(40+w)

but this comes out wrong. I know w should =0, right. Any help would be great

Say we do a 2 dollar increase. According to your definition, w = 1. Therefore the hotel will rent out 150-8*1 = 142 rooms for 40+1=41 dollars per room (!).
Do you see how you should correct your formula now?