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Tickets to a local baseball game cost $5. On average, 350 people attend each week. For every weekly 50-cent increase in ticket price, the number of people decreases by 25 per week. By what amount should the ticket price increase to maximize ticket revenue?

A. $0.50
B. $1.00
C. $1.50
D. $2.00

User Podo
by
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1 Answer

5 votes

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.

User Spyridon
by
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