Q1) The Chicago Opera is setting prices for subscription to next seasons performances and they have hired a consultant. consultant has determined that audience is composed of two kinds of customers. The first are "patrons", who are affluent and committed opera lovers. By studying past demand consultant determines that patron's demand is describeed by equation P_{p} = 450 - .15Q_{p},
where P_{p} is price a patron should pay for subscription and Q_{p} are number of patron subscriptions.
Other group of potential subscribers is "students", who are normally less affluent and less committed to opera. Their demand is given by P_{s} = 300 - .15Q_{s},
where P_{s} is price a student should pay for a subscription and Q_{s} are the number of student subscriptions.
a) Imagine opera has capacity of 3000 seats and that all costs are fixed. If they can discriminate between two groups, determine optimal price to charge to each group and how many tickets will each group buy?
b) If opera can only seat 2000 people and can discriminate compute optimal price to charge to each group and how many tickets will each group buy?
c) If opera has a capacity of 3000 but cannot discriminate (i.e., they should charge same price to everyone). Compute the optimal price?