Paris Hilton, heiress to both the Hilton Hotel and the real estate fortune of her father, was impressed by the recent academic upswing by NUS. And she has opened a modern fitness center next to the NUS Business School building, which would run as a private property. There are 1,000 potential NUS students and 1,000 NUS professors who may be interested in working out at this fitness center. Each visit by a student or a professor costs the center $1 and the center's fixed costs are all sunk. Hilton, not surprisingly, is a profit-seeker throughout all the situations given below.

Each of the NUS professors and students has the following preference for the fitness center facilities:

P = 9 - QP for each professor

P = 9 - 2QS for each student

where P denotes per-visit fee and QP and QS denotes the number of visits to the center per month by a professor and a student, respectively.

Answer the following questions. No need to provide a graph or a diagram.

(1) Suppose that the center can check ID cards to identify if a customer is a student or a professor. Which combinations of monthly membership fee and per-visit fee should the center charge each student and professor, respectively, to maximize the center's profit?

(2) Not surprisingly, given the pricing scheme in (1), professors began to use fake student IDs and Hilton's fitness center was not as profitable as expected. Annoyed by the professors' opportunistic behavior, Hilton asked the center's marketing manager to consider abandoning its discriminating pricing scheme as in (1). Instead, she proposed that the center introduce the following 'common' monthly deal that applies to both customer types, requesting that it should not be in professors' interest to join:

'Allow up to X times of visit to the center per month at the upfront monthly fee of $Y'

The center's marketing manager has contacted you - a proud NUS MBA graduate - and asked for help regarding what level of $X and $Y to follow up with on Hilton's request. What would be your recommendation?