4. Suppose the University of Michigan is considering revising the pricing of its undergrad- uate program. The new tuition structure may include an annual tuition, a charge per course-hour, or both. A study of UM applicants shows that their willingness to pay for a UM education can be stated in terms of a demand for course-hours. Also, UM students can be divided into two groups, \"normal\" students (N) and workaholics (W), in terms of the number of hours they would demand if the School imposed a single charge per course-hour. Each of the normal students demands course hours in the amount: QM = 135 %P where Q is the number of course-hours per academic year and P is the price per course-hour. Each of the workaholics have a demand of: Qw = 180 :P. The school will admit 1000 students from each group. The marginal cost to the school is constant at $30 per student course-hour. UM's xed cost is $20 million per year. Design the following pricing schemes, solving for the prot-maximizing price structure and the total prot. (assume UM's goal is to maximize prots {rather than, e.g., maximizing the number of people that get educations)). (a) A single xed tuition per academic year {with a zero price per course-hour), with no limit on the number of course hours taken by students. (b) A single tuition per academic year plus a single fee per course-hour. (c) A system which discriminates between the two groups, with a 2-part structure of annual tuition and per-hour fees for each. In other words, UM can identify who is a workaholic and who is a normal student, and offer a different two-part tari' depending on which group a student belongs to. Your answer here should be two two-part tariffs, one to offer to the workaholics, and one to oer to the normal students