You have one gym on your campus. The gym is open from 9:00 a.m. until 9:00 p.m. according to university policy, and it cannot be opened any earlier or later. Your assignment is to come up with a policy for allocating time for student and faculty recreational needs and demands and then to assign time slots considering variables such as the number of students participating, setup times for certain sports, and political issues on campus. The gym has two side-by-side basketball courts. When the space is not used for basketball, there can be two volleyball courts or six badminton courts. There can be one volleyball court and three badminton courts set up at the same time, but there is the risk of balls hitting people, so such an arrangement is not encouraged. There can be 12 volleyball players on the court at any time and four badminton players on each badminton court.
The following are the rules you have to work under:

The gym is needed from 2:00 to 6:00 p.m. for athletics; thus, no events can be scheduled during this time frame.
Most students have class in the morning, so they do not have a lot of time early in the day to use the gym.
There are 100 students who want to play recreational basketball, and they can use two courts.
There are 40 students who want to play volleyball, which takes 20 minutes to set up and tear down.
There are 50 students who would like to participate in aerobics.
There are 20 international students who would love to play badminton, which takes 20 minutes to set up and tear down.
Winter is coming and several sports might have to move their players indoors for their workouts when the weather is bad.
There are 10 faculty members who would like to play basketball, but not necessarily with students.