All 80 rooms in a motel will be rented each night if the manager charges $35 or less per room. if he charges $(35+x) per room, then 2x rooms will remain vacant. if each rented room costs the manager $8 per day and each unrented room $2 per day in overhead, how much should the manager charge per room to maximise his profit? solution the number of rented rooms is so that the revenue is . the total cost in overhead is . if no room is rented then 2x=a so that x= while if all rooms are occupied then x=0 since the manager shall have charged $35. thus the profit equation is p(x)= with the domain
