The maximum harmonious party. A successful businessperson wishes to give a party for the local clients of the firm she manages. The firm has many clients (n of them). and the executive wishes to have the largest party possible subject to just one kind of constraint. compatibility.
All the invitees need to get along, or be compatible, and in this case. a number of pairs of clients do not get along, indeed might even get into noisy arguments if they drink too heavily. The executive knows which pairs of clients do not get along, but still wishes to have the largest possible party that can be arranged.
Formulate a zero-one programming problem which, if it could be solved. would select which clients to invite. You are given all the (j, k) pairs that are incompatible. that is. the pairs of clients who cannot get along.