Answer:
Explanation:
To find the optimal ticket price that will maximize revenue, we need to determine the price point where the increase in revenue from selling each ticket at a higher price is greater than the decrease in revenue from selling fewer tickets due to the higher price.
Let's start by calculating the current revenue generated at the current ticket price of $6.00:
Current revenue = 1800 x $6.00 = $10,800
Now, we need to determine the effect of increasing ticket prices by $0.50 on the number of tickets sold:
For each $0.50 increase in ticket price, 100 fewer people will attend. So, for a $0.50 increase, the new ticket price will be $6.50, and the number of attendees will be:
1800 - 100 = 1700
For a $1.00 increase, the new ticket price will be $7.00, and the number of attendees will be:
1700 - 100 = 1600
And so on.
We can create a table to calculate the revenue at different price points:
Ticket Price Number of Tickets Sold Revenue
$6.00 1800 $10,800
$6.50 1700 $11,050
$7.00 1600 $11,200
$7.50 1500 $11,250
$8.00 1400 $11,200
$8.50 1300 $11,050
$9.00 1200 $10,800
As we can see from the table, the optimal ticket price that will maximize revenue is $7.50, where the revenue is $11,250. Beyond this point, the decrease in attendance outweighs the increase in ticket price, resulting in a decrease in revenue.
Therefore, the owner should increase the ticket price to $7.50 to maximize revenue.