A small college is trying to predict enrolment for the next academic year. The vice president for business states that enrolment has tended to follow a pattern described by E = 18,000 - 0.5P, where E denotes total enrolment and P is yearly tuition. a) If the school sets tuition at 20,000, how many students can it expect to enrol? b) If the school wants to maximize total tuition revenue, what tuition should it charge? c) As the vice president for business, what tuition would you recommend? Explain briefly. d) Due to a strong post-COVID-19 recovery, the income conditions in the region improve substantially. Explain in one sentence how this could affect the college's enrolment pattern and the enrolment level maximizing its tuition revenue