A youth soccer club has contracted with Holiday Helpers, a local travel agency, to broker hotel rooms for out-of-town teams that have entered the club's Labor Day weekend soccer tournament.
The agency has 12 teams it needs to arrange rooms for at 8 possible hotels. The following tables show the number of rooms each team needs, the number of rooms available at each hotel, the room rate at each hotel, and the maximum room rate each team wants to pay:

a. All of a team's rooms must be at the same hotel. Formulate a model and develop a solution for the agency to reserve rooms for as many teams as possible, according to their needs.
b. The travel agency has requested that each team indicate three hotels it would prefer to stay at, in order of priority, based on price, location, and facilities. The teams' preferences are shown in the following table:

Determine a revised hotel room allocation to assign rooms to all teams while reflecting their preferences to the greatest possibleextent.

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Max Rooms Rate Needed Hotel Team Available B. Roadside G. Bayside 0. Hurricanes 11. Strikens 20 14 Team Hotel Poity 1 2 3 45 6 78 9 10 11 12 C B C F D F CF H C A E НА 2 G G -HE A G H F BA H B B F D E A