In a popular TV show called The Bachelors, a matchmaker wishes to match each of the four female participants (Cathy, Mary, Nancy, and Susan) with one of the four male participants (Bill, John, Robert, and Sam) so that the number of people who are matched with a compatible pair is maximized. The following compatibility results have been decided according to the viewers’ votes:
Cathy is compatible with John and Robert.
Mary is compatible with Robert and Sam.
Nancy is compatible with Bill, Robert, and Sam.
Susan is compatible with Bill and John.
Explain your strategy for choosing the optimal matching scenario.