The popular a cappella choral group Here Comes Treble is coming to Columbia University for a concert. The concert will be in Lerner Auditorium, which has C seats. Customers can be segmented into students holding a student ID card and the general public. The price-response function for the general public is dg(pg) = (2,400

– 60pg)+, and the price-response function for students is ds(ps) = (400 – 25ps)+.

(Note: If you cannot do part

a, you can assume that C = 1,500 for the following parts.)

a. Columbia plans to sell general admission and student tickets. To find the revenue-maximizing ticket prices, Columbia decides to solve a revenue-maximization problem with the capacity constraint 12pg + 5ps ≥ 320, together with the demand nonnegativity constraints ps ≤ 16 and pg ≤ 40. Given this information, what is the capacity of the auditorium?

b. Given the capacity of the auditorium that you calculated in part

a, what is the revenue-maximizing single price?

c. Columbia decides to go through with the plan of charging different prices for general admission and student tickets. Given the capacity of the auditorium you calculated in part

a, what are the revenue-maximizing ticket prices for students and the general public?

d. Assume that Columbia reschedules the concert for a larger auditorium with 3,000 seats. What are the revenue-maximizing prices for students and the general public?