Maximizing Revenue from Ticket Sales

The video tutorial explains how to determine the ticket price that maximizes revenue for a soccer stadium with a capacity of 40,000 spectators. It uses a linear relationship between ticket price and attendance to derive a quantity function, which is then used to formulate a revenue function. The revenue function is a quadratic equation, and its vertex is calculated to find the optimal ticket price and maximum revenue. The tutorial concludes with a graphical verification of the results.

What is the average attendance when the ticket price is set at $15?

• 28,000

• 40,000

• 30,000

• 34,000

How is the revenue from ticket sales calculated?

• Price of tickets plus quantity sold

• Price of tickets minus quantity sold

• Price of tickets times quantity sold

• Price of tickets divided by quantity sold

What is the slope of the line used to derive the quantity function Q(P)?

• -2,000

• -1,000

• 1,000

• 2,000

What is the y-intercept of the quantity function Q(P)?

• 34,000

• 12,000

• 58,000

• 28,000

What type of function is the revenue function R(P)?

• Quadratic

• Logarithmic

• Exponential

• Linear

What ticket price maximizes the revenue according to the vertex of the parabola?

• $15.00

• $13.00

• $14.50

• $12.00

What is the maximum revenue that can be achieved?

• $450,000

• $430,000

• $400,000

• $420,500

How many tickets are sold at the price that maximizes revenue?

• 34,000

• 29,000

• 28,000

• 30,000

What is the significance of the vertex in the context of this problem?

• It indicates the minimum revenue.

• It determines the ticket price that maximizes revenue.

• It provides the average ticket price.

• It shows the maximum attendance.

How can the results be verified graphically?

• By comparing different ticket prices

• By checking the slope of the line

• By plotting the revenue function and checking the vertex

• By calculating the average attendance