1. (5 points) Optimal arrangement for a company retreat You are organizing a big dinner party for your company retreat. To increase social interaction among the various departments in your company, you would like to set up a seating arrangement so that no two members of the same departments are at the same table. Show how to formulate the problem of nding a seating arrangement that meets this objective as a maximum ow problem. Assume that the company has n departments and the ith department has mi members. Also assume that t tables are available and the jth table has a seating capacity of cj .