3. [20 Points Several families go out to dinner together. To increase their social interaction, they would like to sit at tab

3. [20 Points Several families go out to dinner together. To increase their social interaction, they would like to sit at tables so that no two members of the same family are at the same table. Show how to find a seating arrangement that meets this objective (or prove that no such arrangement exists) by reducing this problem to MAXIMUM FLow. Assume that the dinner contingent hasp families, that the ith family has ai members, that q tables are available and up to bj people can be seated at table j. (a) Define the network that you want to use. (b) Explain why max flows in your network solve the problem at hand. (And show where you use the integrality of max flows) (c) Analyze the running time of your algorithm



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