A local university charges in-state and out-of-state students different tuition rates. In-state students pay $3500 a term and their demand is given by QI = 45,000 - 4TI where QI = in-state student enrollment and TI = in-state tuition. Out-of-state students pay $5000 a term, and their demand is: QO = 25,000 - 4TO where QO = outstate enrollment and TO = outstate tuition. a. Calculate the number of each type of student that will enroll, and the total enrollment at the university. Also calculate price elasticity for each type of student. b. Assume that marginal cost for students is $3200. Is the university charging an optimal tuition rate for in-state students? Explain.