Each year a new group of high school seniors chooses where they want to attend college. The University of Kentucky faces two identifiably different categories of customers, in-state and out- of-state students. The (inverse) demand equation for in-state students is given by PI =$9000- QI, while demand by out-of-state students is given by PO = $21,000 -9Q O . P represents the annual tuition charged by UK and Q represents the number of students who enter as freshmen. The marginal cost of educating an additional student is constant and equal to $3000. Suppose that the Board of Trustees wants to act as a profit-maximizing monopolist in setting price and output. What tuition should they charge for in-state and out-of-state students, and how many of each would enroll each year? Illustrate your answer in the diagram below