Optimizing profits

Mathematicians like space. Like in vector space, metric space, topological space. In fact, any set with structure can be called a space. In "simple" Euclidean geometry there are all sorts of problems of how to fill a space with as much objects as physically possible. How many spheres of a certain radius can we store in a cube? And so forth. - The Japanese people excel in many areas: architecture, technology. This combined with the special conditions ( a lack of =space= ) in Tokyo lead to extraordinary inventions. The following =must= have been the solution to an optimization problem of some kind. Like maximize the number of hotelrooms ( they must have started with rooms in mind ) given a number of constraint. Or simply maximize profits because I bet this 'cheap' hotel is making more profits than their five star competitors. Thanks to optimization and applied mathematics. No matter how much they love space mathematicians can minimize it for you.



I am Dutch, so somewhat exposed to overpopulation and too many people on limited ( office ) space. I can comfortably stay in any hotel though, no matter how smallish the room.  Not even the German U-boat movie 'Das Boot' gave me the same feeling of claustrophobia.