Question: Problem 4 - Bipartite Matching: OpenTable is managing the dinner reservations at a restaurant. There are n tables available for reservations, numbered as 1, 2,

Problem 4 - Bipartite Matching: OpenTable is managing the dinner reservations at a restaurant. There are n tables available for reservations, numbered as 1, 2, ...,m. Assume (for simplicity) that each table can only accommodate one dinner reservation. Tables have different sizes: table j can sit tj customers. There are n requests for a reservation, numbered 1, 2, ..., n. Reservation i is for a group of ri people. Due to unforeseen circumstances, the restaurant cannot accommodate all the reservations and some of them have to be canceled. (a) Formulate the problem of maximizing the number of customers that we can accommodate as a binary programming problem (not as a bipartite matching problem). (b) Consider the problem of maximizing the number of reservations that we can accommodate. Discuss how this problem fits the framework of the Bipartite Matching problem. Draw a sample network for this problem. What are the nodes, the arcs, and the arc capacities?

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