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Suppose that to be able to buy lunch at McGill University's Faculty Club, a professor must pay a yearly membership fee of L dollars. Once a professor is a member, he/ she can buy a standard lunch at the price of p (set by the Faculty Club). Assume that there are two types of professors: old professors, and young professors. The inverse demand function of a typical young professor is p=72Q1 where ql is quantity of lunches (at the Faculty Club) demanded by a young prcr fessor per year, and p is the Faculty Club's xed price for each lunch. The inverse demand function of a typical old professor is P=92q2 where Q2 is quantity of lunches (at the Faculty Club) demanded by an old professor per year, and p is the Faculty Club's xed price for each lunch. The university's regulation is that the Faculty Club cannot charge discriminatory lunch prices, and cannot charge different membership fees for different customers. Assume there are 10 young professors and 10 old professors. The Faculty Club wants to maximize its prot. The Faculty Club's marginal cost of a lunch is $25 and it is required that the price p be not less than the marginal cost. (i) Find the protmaximizing solution 13* and L". Find the Faculty Club's total prot. (10 marks.) (ii) Suppose there is a change in preferences, such that a typical young profes sor's demand is now lower than before: 19:5241 Under this preference scenario, What are the Faculty Club's optimal membership fee, L, and xed price per lunch, p, for members? What is the Faculty Club's total prot? (10 marks.)