I'd like to start off by noting that cellphone billing is very different from that in the US. The consumer is free to choose any cellphone he wants and he still has a choice for the carrier/telecom service provider. This is the reason why unlike in the US, providers in India depend on earning the patronage of particular demographics through customized plans for them. DIfferent plans for collegians, for people who want just incoming calls, people who have to make a lot of short calls etc. - - - - - - - - - - - - - - - - - I am quoting the problem statement verbatim - the next post will elucidate the solutions that I am working on. The primary question here is : What branch of mathematics and WHAT topic should I refer so that I can attempt this question methodically?