Valley United Soccer Club has 16 boys' and girls' travel soccer teams. The club has access to

Question:

Valley United 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, whereas field 2 has enough room for only one team. The teams practice twice per week, either on Monday and Wednesday from 3 P.M. to 5 P.M. or 5 P.M. to 7 P.M., or on Tuesday and Thursday from 3 P.M. to 5 P.M. or 5 P.M. to 7 P.M. Field 3 is in the worst condition of all the fields, so teams generally prefer the other fields; teams also do not like to practice at field 3 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 available only after work. Some teams also prefer specific fields because they're closer to their players' homes. Each team has been asked by the club field 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 P.M. to 5 P.M. on Monday and Wednesday as its top priority, field 1 from 3 P.M. to 5 P.M. on Monday and Wednesday as its second priority, and so on.
Formulate and solve a linear programming model to optimally assign the teams to fields and times, according to their priorities. Are 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 time 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 be at practice only at 5P.M.?