Final answer:
To maximize ticket revenue, the ticket price should increase by $1. The correct answer is option B.
Step-by-step explanation:
To maximize ticket revenue, we need to find the price that will result in the highest total revenue.
We can start by calculating the revenue at the current price of $5 per ticket and 350 people attending.
The revenue is calculated by multiplying the price by the number of people. So, the current revenue is
$5 x 350 = $1750.
Now, let's consider the effect of a 50-cent increase in ticket price.
We know that for every 50-cent increase, the number of people attending decreases by 25 per week.
So, if we increase the ticket price by 50 cents, the new price per ticket would be
$5 + $0.50 = $5.50,
and the number of people attending would be
350 - 25 = 325.
The new revenue would be
$5.50 x 325 = $1787.50.
We can repeat this calculation for the other options and compare the revenues to determine which one maximizes total revenue.
By increasing the ticket price by $1, the revenue would be
$5 + $1 = $6 per ticket, a
nd the number of people attending would be
350 - (25 x 2) = 300.
The new revenue would be
$6 x 300 = $1800.
If we further increase the ticket price by $1.50, the revenue would be
$5 + $1.50 = $6.50 per ticket,
and the number of people attending would be
350 - (25 x 3) = 275.
The new revenue would be
$6.50 x 275 = $1787.50.
Finally, if we increase the ticket price by $2, the revenue would be
$5 + $2 = $7 per ticket,
and the number of people attending would be
350 - (25 x 4) = 250.
The new revenue would be
$7 x 250 = $1750.
Based on these calculations, it is clear that increasing the ticket price by $1 would maximize ticket revenue, as it results in a revenue of $1800.