please explain how to solve the 3 parts in details

We are given two groups of consumers. 1) Students have a demand given by P3 = 6 qs 2) Professors have demand given by Pp = 12 - qp Here, q is the quantity demanded by one consumer per month. The firms marginal cost is MC: 0 1. Suppose the movie theater can observe the type of consumer and offers two packages with quantity qt- at xed monthly fee Fa, what quantities and fees maximize the rm's prots? (Take into account we don 't need to compute the price for a ticket, but a fee to enter to the movies 13,- 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 di'erent types of consumers? Does this make sense if there is the same proportion of Students and Professors