The price per day & per unit is 50+X.
The profit of each occupied room is (50+X)-4=46+X, where 4 is the cost for cleaning and supplying.
So the number of occupied rooms is 280-2X (each time you increase of 1$, there are 2 vacancies).
We assume that an empty room makes no profit.
Therefore, the total profit is P(X)=(46+X)(280-2X)=-2X²+188X+12880.
We want it to be maximum.
--> , which annulates at X=188/4=47.
So the price of the rooms has to be 50+47=97.
I hope I didn't make any mistake