Ticket Price Investigation
Angelina Katsanis
Introduction
In this problem, the student government is trying to find the ideal price of a ticket that would allow access to all the athletic events at their school. To find the ideal price, the maximum possible revenue must be identified. In a survey, parents were asked how much they would pay for one of these tickets. With the data collected from that survey, the ideal ticket price was found. Below are the results from the survey to the parents.

Methods
Create simple equation to model revenue collected from the ticket price multiplied by the amount of people buying tickets
R = xy
R = Revenue
X = ticket price
Y = number of people that would buy the tickets
Use linear regression to create a line from the data points
Y = -5.08x + 996.85
Substitute linear equation above into the first equation determining revenue to create a quadratic equation
R = x(-5.08x + 996.85)
Distribute the x to create the final equation R = -5.08x2 + 996.85x
Find the coordinates of the maximum of final equation
X is the ideal ticket price, y is the total revenue that would be earned
Weaknesses
The idea that parents may change their mind when the payment is no longer theoretical was not taken into account
There is no way to know if every single parent took the survey. Or, if everyone was forced to, if they were all honest
Conclusion
To get the maximum revenue from the tickets, the student government would have to sell them for $98.12. This would mean that a total of about $48,903.05 would be earned. These numbers were drawn from the maximum of the parabola created by the equation R = -5.08x + 996.85x. The exact coordinate of the maximum is (98.115, 48903.047).