A basketball or some stadium holds 20000 people. On average 140000 come to see the match. Average ticket price is $75. market research shows that if ticket price is decreased by $5 800 more people buy tickets. Find the price that will maximize revenue and find maximum revenue?
It would help if you proofread your questions before you posted them.
Is 20,000 missing a zero, or does 140,000 have an extra zero?
To find the price that will maximize revenue and the maximum revenue, we need to analyze the effects of changing the ticket price on the number of tickets sold and the total revenue.
Let's start by assuming the ticket price is P dollars. According to the problem, when the ticket price is decreased by $5, 800 more people buy tickets compared to the original scenario.
So, the number of people who buy tickets at the original price, P, is given by:
Original number of ticket buyers = 140,000
When the price is decreased by $5, the number of ticket buyers increases by 800:
Number of ticket buyers at decreased price = 140,000 + 800
Now we have all the information needed to calculate the total revenue.
The total revenue is given by the product of the number of ticket buyers and the ticket price:
Original revenue = P * 140,000
Revenue at decreased price = (P - 5) * (140,000 + 800)
To find the price that maximizes revenue, we can set the two revenue expressions equal to each other and solve for P:
P * 140,000 = (P - 5) * (140,000 + 800)
Simplifying the equation:
140,000P = (P - 5) * (140,800)
Expanding:
140,000P = 140,800P - 5 * 140,800
Simplifying further:
140,000P = 140,800P - 704,000
Rearranging the equation:
704,000 = 140,800P - 140,000P
Combining like terms:
704,000 = 800P
Dividing both sides by 800:
P = 880
Therefore, the price that will maximize revenue is $880.
To find the maximum revenue, substitute this price back into one of the revenue expressions:
Maximum revenue = 880 * 140,000
So, the maximum revenue is $123,200,000.