I have that problem in my mind and cannot figure out how to solve it, the problem as follow:

Given n clients (1 - n) , m shops and every shop can serve a set of clients (this set is given in the input), so maybe the client can be served by more than one shop, what is the minimum number of shops that can cover(serve) all clients?

I thought about max flow but I failed to come up with the solution.. I know that min cost algorithm will pay for every flow a specific cost, could I modify the algorithm so every X flow will pay only (1) cost?

Any ideas?