2008-09-10

The Hotel Manager

Bengt is thinking about getting a job. He thinks it would be cool to be a hotel manager. This is obviously never going to happen, because Bengt is far too lazy to be a hotel manager, possibly too lazy for any job at all, but he still likes to think about it. But he can't decide what would be the optimal ratio between single and double rooms in the hotel.
Whenever guests arrive at the hotel, there is a probability p that it is a couple, and a probability 1-p that it is a single person. A single person can occupy any room, either a single or a double. A couple can occupy one double room, or (although it might make them somewhat dismayed) they can occupy two single rooms. A double room is d times bigger than a single room, and there is only a certain amount of space in which to build rooms.

    To avoid as far as possible having to turn guests down, which fraction of the rooms should be double rooms?