A sweet problem - Colegiul National C. Negruzzi (Iași - Roumanie)

We had an interested problem, related to a cake as a cuboid, which had to be served by 100 persons at a birthday party. The person who celebrates his birthday has to cut the cake such that everybody who is there can eat a piece in order to taste the sweet cake. Pieces can be every shape or size; they do not have to be equal, but they cannot be rearranged after any cut. The cake can be cut every direction. We found out the minimum number of cuts the celebrated person should do in order to satisfy all guests (everybody tastes the cake), the minimum number of cuts in order to get equal pieces, the dimensions of the cake that has maximum volume.