<s>[INST] A university is planning to offer a new major in Data Science. To be successful, the program needs to attract at least 40 students and also have at most 20 students in each course. Course sizes are fixed at either 16 or 20 students. The Data Science program requires students to take the following courses:
- Course A: Required for all students
- Course B: Required for all students
- Course C: Required for all students taking A and/or B
- Course D: Required for all students taking A, B, AND C
- Course E: Required for all students taking (A AND B AND C) OR A AND D)
What are the initial enrollments for Course A and Course B and how many students need to enroll in Course A such that the program can offer Course E?
- What is the minimum initial enrollment in Course A?
- What is the minimum initial enrollment in Course B?
- How many students need to enroll in Course A such that the program can offer Course E?[/INST]