When the ticket price for a concert at the Arias Magnificas Opera House was $50, the average attendance at concerts at that price was 4012 people per concert. When the ticket price was raised to $52, the owners found that the concert attendance dropped to an average of 3828 people per concert. The aim of this group project is to find the correct ticket price to maximize the revenue from a concert.
1. Assuming that demand (the average number n of tickets bought) is a linear function of the average ticket price, find an algebraic expression n = f(p) for the demand as a function of the ticket price p. Identify clearly what your variables represent.
2. Find the total revenue R(p) from tickets sold as a function of price p (where p is the only independent variable).
3. What is the ticket price that the owners should set to guarantee a maximum revenue?