Final answer:
To find the ticket price that maximizes revenue for a baseball team, we need to locate the vertex of the parabolic revenue function on a downward-sloping demand curve. By averaging the two given points, we find that the optimal ticket price is $10.50.
Step-by-step explanation:
To determine what ticket price would maximize revenue for a baseball team with a linear relationship between price and attendance, we need to understand the concept of demand elasticity. If the band mentioned in the example faces a downward-sloping demand curve, this means that increasing ticket prices will lead to a decrease in the number of tickets sold. To maximize revenue, the band (or in the student's question, the baseball team) needs to find the ticket price that results in the highest product of the price and the number of tickets sold, considering the elasticity of demand.
In the student's case, we have two points that can be used to form a linear equation: (12, 28000) and (9, 33000), where the first value of each pair is the ticket price in dollars and the second value is the average attendance. The goal is to find the price that maximizes the revenue function R(p) = p × attendance(p), where p is the ticket price.
To maximize revenue, it is necessary to find the vertex of the parabolic revenue function, which is located at the midpoint between the two given points on the demand curve. This is calculated by finding the average of the two ticket prices. In this case, the ticket price to maximize revenue would be the average of 12 and 9, resulting in $10.50.