I would like to know how to approach this problem from 1 to 3.

4 Problem 4 The only movie theater in Westwood is facing two groups of consumers. Students have relatively low demand given by p3 = rm and Professors have relatively high demand pp = 12qp , where q,- is quantity demanded by one consumer per month, i{S, P}. The rm's marginal cost is M0 = 0. 1. Suppose the movie theater can observe the type of consumer and offers two packages with quantity q,- at xed monthly fee Fr, what quantities and fees maximize the firm's prots? (Take into account we don't need to compute the price for a ticket, but a fee to enter to the movies q,- times in a month). 2. Now suppose that the theater is not able to distinguish the types, would the pricing scheme from part (1) work if the movie theater kept offering the same packages? 3. Now the movie theater wants to offer two different packages with quantities you found in part (1). The theater is still unable to distinguish the consumer type. What monthly fees should it charge to he different types of consumers? Does this make sense if there is the same proportion of Students and Professors