The Metro Soccer Club has 16 boys and girls travel soccer teams. The club has access to three town fields which its teams practice on in the fall during the season. Field 1 is large enough to accommodate two teams at one time, and field 3 can accommodate three teams, while field 1 only has enough room for one team. The teams practice twice per week, either on Monday and Wednesday from 3 to 5 or 5 to 7, or on Tuesday and Thursday from 3 to 5 or 5 to 7. Field 3 is in the worst condition of all the fields so teams generally prefer the other fields, and teams also do not like to practice there because it can get crowded with three teams. In general, the younger teams like to practice right after school while the older teams like to practice later in the day. In addition, some teams must practice later because their coaches are only available after work. Some teams may also prefer a specific field because it€™s closer to their player€™s homes. Each team has been asked by the club coordinator to select three practice locations and times in priority order, and they have responded as follows.

For example, the under-11 boys age group team has selected field 2 from 3 to 5 on Monday and Wednesday as their top priority, field 1 from 3 to 5 on Monday and Wednesday as their second priority, and so on. Formulate and solve a linear programming model that will optimally assign the teams to fields and times according to their priorities. Were any of the teams not assigned to one of their top three selections? If not, how might you modify or use the model to assign these teams to the best possible and location? How could you make sure that the model does not assign teams to unacceptable locations and times€”for example, a team whose coach can only be at practice at5?

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