Enormous College is a liberal arts college. The college wants to simulate next year's budget planning. There is an application fee of $250. If the application is rejected, the college refunds the fee. Hence, the application fee is charged to students who are admitted. Once the admission is given around mid-March, students have some time to make a decision. When they accept the offer, students must submit an acceptance form. In the past, this acceptance rate was 80%. The college receives an application from the students who accepted the offer for on-campus housing by the end of May, which is first come first served. The maximum number of students who live on campus is 300 but the college accepts more than 300 applications. Also, the cost of "room and board" for students is $5,000 and the tuition is $70,000 per year. The administrative cost is assumed to be 60 million dollars and the total cost of on-campus housing is 1.5 million dollars. a) What is the average profit? b) On average, is running an on-campus housing profitable? c) If the average target profit from on-campus housing is 2 million dollars, What should be the new "room and board" charge?