After graduating, your consulting career leads you to a position advising a nationwide chain of movie theaters. After some research, you learn that your theater chain serves primarily two types of customers: Professionals and Students. The number of each type coming to any showing of a movie depends on the price of a ticket, of course. Professionals attend according to the demand function = 480 20p, while students attend according to the demand function = 480 40p. Currently, the chain has set ticket prices at $10 per ticket. Theaters are seldom at capacity, so there is no marginal cost to allowing another moviegoer to attend. a. (2 points) How many Professionals come to each movie? b. (2 points) How many Students come? c. (3 points) What are the theater's profits for each showing? d. (5 points) What is the profit-maximizing price? (Hint: It's not $10) e. (4 points) If the theater chain changes the price of a ticket to the profit-maximizing price, how many of each type will attend? f. (3 points) What are the theater chain's profits per showing now?

Fondly recalling your days in graduate school, you have an idea: What if the theater offered a student discount to moviegoers with a valid student ID? Only Students have ID's.

g. (5 points) What is the profit-maximizing price to charge each type of consumer? h. (3 points) What are the theater's profits per showing in this situation? i. (3 points) Some of your theater locations are not proximate to a school, and so while the Professionals' demand remains = 480 20p at these locations, the Student demand is = 120 10p for some theaters. How should you change your recommended pricing strategy for these locations? Explain