Final answer:
Without the specific pricing expression for when more than 10 people take the tour, we cannot calculate the ticket cost for 15 people. The elasticity of demand for tickets influences whether raising prices will increase revenue, with bands needing to balance ticket price and sales volume for maximum revenue.
Step-by-step explanation:
The price per ticket for a tour company changes depending on the number of people who take the tour. If more than 10 people take the tour, the pricing structure shifts from a flat rate to a variable rate based on the number of participants, n. However, the specific expression for the price per ticket when more than 10 people take the tour is not provided in the question. Therefore, to answer the question about how much a ticket costs if 15 people take the tour, we would need that expression.
Concerning the revenue generation, the scenario of whether raising prices can increase revenue depends on the elasticity of demand. For a band on tour, if the demand for tickets is inelastic, they might raise prices without significantly reducing the number of tickets sold, potentially maximizing revenue even with a non-full arena. However, if demand is elastic, setting a ticket price too high would lead to fewer sales, decreasing overall revenue. The optimal strategy would need to balance ticket price and the number of tickets sold to achieve maximum total revenue.