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:

Team Max Rate Rooms Needed Hotel Room Rate Rooms Available 1. Arsenal $ 70 15 A. Holiday $ 90 41 2. United 75 18 B. Roadside 75 26 3. Wildcats 60 20 C. Bates 55 38 4. Rage 80 12 D. Hampson 95 25 5. Rapids 110 17 E. Tilton 100 26 6. Storm 90 10 F. Marks 80 38 7. Tigers 70 18 G. Bayside 70 35 8. Stars 80 18 H. Harriott 80 52 9. Comets 80 20 10. Hurricanes 65 16 11. Strikers 90 20 12. Bees 100 14

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:

Hotel Priority Team 1 2 3 4 5 6 7 8 9 10 11 12 1 C B C F D F C F H C A E 2 G G — H E A G H F — H A 3 — C — B A H — B B — F D Determine a revised hotel room allocation to assign rooms to all teams while reflecting their preferences to the greatest possible extent.

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