Given a set D dogs, C cats, and B birds, for each dog d in D, there is a set c(d) which indicates the set of cats that dog d likes and a set b(d) birds that dog d likes. How do I find the maximum number of groups that can be formed with one dog, one cat, and one bird s.t. the dog is likes both the cat and bird (max 3 animals in one group)?
I am thinking about using linear programming, but I am really quite unsure about how to approach this problem. Does anyone have any insight?