I am quite familiar with Ford-Fulkerson algorithm but I am having a trouble to apply the algorithm to the following problem. Can someone please give me some hints or better instructions how to use FF method to this problem?
Let O be a set of n objects. It is required to form a set G of m groups. There are three possibly overlapping subsets of objects: A, B and C. Each object belongs to one or more of these subsets. Each object can be assigned to at most one group. It is required that every group must have at least ten objects: two are from subset A, three others are from subset B, and one other is from subset C; the remaining objects can be from any subset.
It is required to explain how to apply the Ford-Fulkerson algorithm to determine whether it is possible to assign n objects to m groups according to the given rules.
Small addendum (See below the idea suggested by @D.W.): In case of only two subsets A and B, the flow network could look like that (?). I assume that capacities c1, c2, c3 can be found from subset A and B