Hotel Before the new soccer seasons starts, 7 Turkish super league teams are planning to go...

 

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Hotel Before the new soccer seasons starts, 7 Turkish super league teams are planning to go to Antalya to prepare for the new season. The teams are contracted for a travel agency to arrange them for the hotels. There are 6 possible hotels in Antalya. 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 team wants to pay: Team 1. Fenerbahce 2. Galatasaray 3. Besiktas 4. Trabzonspor 5. Sivasspor 6. Kasimpasa 7. Malatyaspor 1. Tilton 2. Holiday 3. Harriot 4. Triple Three 5. Bed and Breakfast 6. Zyatt (ii) Max Rate. $110 (iv) (v) $95 $90 $100 $75 $85 $80 Rooms Needed $55 $85 18 15 20 8 12 10 7 Room Rooms Rate $80 $95 $70 $100 Available 36 20 14 25 In addition, the agency is subject to the following constraints 20 22 A team can either be fully booked or not booked at all. It is not allowed to partially book the teams. (For example, Fenerbahce can be booked for 18 rooms or for no rooms at all.) One team can be booked at multiple hotels. (For example, Fenerbahce needs 18 rooms and 7 of these rooms can be booked in one hotel and the remaining can be booked in other hotels.) A team can only be booked in hotels whose room rate is less than the maximum rate the team is willing to pay. The agency cannot book rooms for Fenerbahce and Galatasaray at the same hotel. Masut Ozil (a player of Fenerbahce) does not want to stay at Bed and Breakfast. The travel agency wants to maximize its revenues from booking the rooms during the season. Formulate a mathematical program to achieve this objective while satisfying the requirements above. (27 Points) Hotel Before the new soccer seasons starts, 7 Turkish super league teams are planning to go to Antalya to prepare for the new season. The teams are contracted for a travel agency to arrange them for the hotels. There are 6 possible hotels in Antalya. 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 team wants to pay: Team 1. Fenerbahce 2. Galatasaray 3. Besiktas 4. Trabzonspor 5. Sivasspor 6. Kasimpasa 7. Malatyaspor 1. Tilton 2. Holiday 3. Harriot 4. Triple Three 5. Bed and Breakfast 6. Zyatt (ii) Max Rate. $110 (iv) (v) $95 $90 $100 $75 $85 $80 Rooms Needed $55 $85 18 15 20 8 12 10 7 Room Rooms Rate $80 $95 $70 $100 Available 36 20 14 25 In addition, the agency is subject to the following constraints 20 22 A team can either be fully booked or not booked at all. It is not allowed to partially book the teams. (For example, Fenerbahce can be booked for 18 rooms or for no rooms at all.) One team can be booked at multiple hotels. (For example, Fenerbahce needs 18 rooms and 7 of these rooms can be booked in one hotel and the remaining can be booked in other hotels.) A team can only be booked in hotels whose room rate is less than the maximum rate the team is willing to pay. The agency cannot book rooms for Fenerbahce and Galatasaray at the same hotel. Masut Ozil (a player of Fenerbahce) does not want to stay at Bed and Breakfast. The travel agency wants to maximize its revenues from booking the rooms during the season. Formulate a mathematical program to achieve this objective while satisfying the requirements above. (27 Points)

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