A large corporation is planning to throw a large party for their clients. The corporation has many clients $($ of them$)$ and they wish to have the largest party possible subject to one simple constraint, guest compatibility. All the invitees need to get along, or be compatible, and in this case, several client pairs do not get along. The corporation knows which client pairs do not get along. Formulate a math program which, if it could be solved, would select the clients to invite that would maximize the number of guests. Hint: Define a parameter that indicates whether a client pair gets along or not.