Linear Programming!

In a miniature university department courses are to be scheduled. Here are the facts what we know:

• There are 6 time slots, 10 courses, 5 professors, 15 students, and 4 classrooms.
• Which professor will offer which course is given as a 5x10 binary matrix.

P=[1100000000;

0011000000;

0000110000;

0000001100;

0000000011];

• Which student will take which course is given as a 15x10 binary matrix.

S=[1101000000; 0010100100;

0010100100;

0010100100;

0010100100;

1101000000;

0000011001;

0000011001;

0000011001;

1101000000;

1101000000;

0000001011;

0000001011;

0000001011;

0000001011];

• Here are the constraints:
• 1. To same place and time, we can schedule at most one course.
• 2. All courses takes two time slots

3. A course cannot be scheduled to two different places at the same time (no sections)

4. A professor cannot be in two different lectures at the same time

5. A student cannot be in two different lectures at the same time (we assume that attendance is absolutely mandatory in all courses, so we cannot allow overlaps in student schedules, as well).

Help me out with this problem, please. The Model will be implemented using julia language