DrexelBoard wants to start a hoverboard sharing service in Philadelphia (much like Zipcar, only with hoverboards instead of cars). There are two types of potential customers: young professionals, each of whom has annual demand that is given by Qprof = 50 – 2p, and students, each of whom has annual demand that is given by Qstudent = 25 – p. In each case, Q is measured in ten minute increments of hoverboard rental time and p is the price in dollars. DrexelBoard’s cost function is 5Q, where Q = Qprof + Qstudent. Assume that there is only one young professional and one student in the market (the results you will find would generalize to any number of users, as long as they existed in equal proportions). (a) Suppose that DrexelBoard was interested in instituting a two-part tariff only for the young professional in which it charges an annual membership fee for the right to purchase hoverboard rental time from the company as well as a usage fee for each ten minute rental purchased. What would be the profit-maximizing membership fee and the usage fee to charge the young professional? (b) What would be DrexelBoard’s economic profits if it only served the young professional using the two-part tariff you solved for in part (a)? (c) Show mathematically and explain in words why the student would not be willing to pay the membership and usage fee you solved for in part (a). (d) Solve for the profit-maximizing two-part tariff (i.e., the membership fee and usage fee) that both the student and the young professional would be willing to purchase. Round your answers to the nearest cent. (e) Putting both the young professional’s and the student’s demand curves in the same graph (with price on the y-axis and quantity on the x-axis), illustrate the two-part tariff you derived in part (d). (f) What are DrexelBoard’s economic profits with the two-part tariff you derived in part (d)? Comparing these profits to those DrexelBoard earned from only serving the young professional (derived in part (b)), should DrexelBoard price to sell to both consumers or just to the young professional?