Hello, I'd like to know the name of the problem (or a similar problem) that I state below: 

Suppose we have a finite set of positive integers. I need to find all the subsets of integers whose sum is less than a constant C and I'd like these sets to be maximal: such that adding any other integer to that set would cause it to overgrow the constant C.

It seems to be fundamental problem and there should be a name for it!

Any ideas?