Question

An arena has 8,848 seats. All seats are sold if the rate of tickets cost $32 each. For each $6 increase, 204 fewer seats ar sold. What is the maximum revenue? Round to the nearest whole dollar.

Answer 1

To find the maximum revenue, we need to determine the ticket price that will result in the highest number of seats sold. We can set up an equation and create a table to find the ticket price and number of seats sold. The maximum revenue is approximately $283,136.

Step-by-step explanation:

To find the maximum revenue, we need to determine the ticket price that will result in the highest number of seats sold. We are given that for each $6 increase in ticket price, 204 fewer seats are sold. Let's set up the equation:

Number of seats sold = Total seats - (Number of $6 increases x 204)

Let x represent the number of $6 increases. The ticket price can be represented as $32 + ($6 x x). The number of seats sold will be: 8848 - (x x 204). To maximize revenue, we need to find the value of x that maximizes the number of seats sold. We can create a table to find the maximum value:

xTicket PriceNumber of seats sold0$3288481$3886442$4484403$508236

As we can see, the number of seats sold decreases as the ticket price increases. Therefore, the maximum revenue will be achieved when no $6 increases are made (x = 0). The ticket price will be $32, and the number of seats sold will be 8848.

To calculate the maximum revenue, we multiply the ticket price by the number of seats sold: $32 x 8848 = $283,136. Therefore, the maximum revenue is approximately $283,136.