A small university has an indoor arena for sporting events that holds 10,000 people. They know that they have 2 distinct segments of customers: students and the general population. Student demand is equal to 2000-125*price and the general population demand is equal to 12000-300*price. They ran an optimization model to determine optimal prices to set assuming that they charge one price to students and one to the general population. They found:

Student price=$8

General Population price=$20

1. What is their current optimal revenue?

2. The university knows that their screening process for the purchase of student tickets is not perfect. They estimate that at any given sporting event, 15% of the general population will wind up purchasing a ticket at the student price rather than the general population price. How can they account for this in a model to resolve for optimal prices?

3. They have solved a new optimization model to find optimal student and general population prices making the appropriate adjustments to the model. They found that they should charge:

Student price=$11

General population price=$19

How much revenue is lost due to the cannibalization of student tickets?

4. The university wants to consider going back to a single price for all tickets. If they resolve the optimization model to only have a single price, they would charge $20 per ticket. Would they sell to any students at this price?

5. Based strictly on the revenue they would earn with a single price compared with the revenue they would earn with 2 prices under cannibalization, should they charge one price or two?

One price ($20 for all tickets)

2 prices ($19 for general population and $11 for students)