You are planning an orientation banquet for incoming summer interns at your company, and one of your jobs is to design the seating chart for the banquet. The intern group includes students from n different schools, and there are a; students from each school iЄ [n]. The banquet will take place at a venue with m tables of various sizes, and each table jЄ [m] can seat h; people. The only constraint is that, in order to facilitate networking, no two students from the same school can sit at the same table.
Suppose that you only know the number of students from each school, but not their names. Model the problem of creating the seating chart as a maximum flow problem. You do not need to draw the network, but be sure to define the full set of nodes and arcs as well as the arc capacities.
