Hotel Charges

Joseph Malkevitch
Mathematics Department
York College (CUNY)
Jamaica, New York 11451

A hotel has software that draws on a simple formula for one person or a family using one of its rooms. However, it has encountered problems when during conventions the hotel is used by people who share a room in quickly determining the final bill for its clients. Here are more details about some of the situations to be handled.

Two clients are to share a room and each of them must provide a deposit. The hotel charges rate r when a single client uses a room but R when two clients share a room. The clients share the room for a certain number of days but one of the clients may arrive or depart before the other. Also the clients send in deposits independently which may not be identical in size.

Develop formulas, in preparation for creating appropriate computer algorithms for the situation above, where the formulas will determine the additional amount to be charged to each client's credit card for the unpaid balance, or provides a refund when appropriate.

What other situations that might occur might also be modeled?