The grand theater is a movie house in a college town. if the theater is open, the owner has to pay a fixed nightly amount of $200 for films, ushers, and so on, regardless of how many people come to see the movie. if the theater is closed, the owner incurs no costs. the nightly demand for movies by students is qs = 180 − 45p and by nonstudent moviegoers is qn = 100 − 5p. (a) assume the grand theater charges a single price to everybody. what is the profit maximizing price and how many tickets are sold to students and nonstudent moviegoers? (b) suppose the cashier can separate students from nonstudents at the door by making students show their id cards and students cannot resell their tickets. then the grand theater can increase its profit by charging students and nonstudents different prices. what prices will the grand theater charge and how many tickets will be sold to students and nonstudent moviegoers? (c) suppose that the grand theater can hold only 90 people and that the cashier can separate students from nonstudents at the door. what prices will the grand theater charge now? how many tickets will be sold to students?