1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
devlian [24]
2 years ago
10

A baseball team plays in a stadium that holds 54,000 spectators. With the ticket price at $10, the average attendance at recent

games has been 21,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000.
(a) Find a function that models the revenue in terms of ticket price. (Let x represent the price of a ticket and R represent the revenue.) R(x) = _________
(b) Find the price that maximizes revenue from ticket sales. $______________
(c) What ticket price is so high that no revenue is generated? $___________
Business
1 answer:
belka [17]2 years ago
5 0

Answer:

a) R(x) =  51000 x - 3000 x²

b) When the Revenue is maximum, The price is $ 8.5

c) When No revenue is generated, The price of the ticket is $17

Explanation:

Given - A baseball team plays in a stadium that holds 54,000 spectators. With the ticket price at $10, the average attendance at recent games has been 21,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000.

To find - (a) Find a function that models the revenue in terms of ticket price.  

              (b) Find the price that maximizes revenue from ticket sales.  

              (c) What ticket price is so high that no revenue is generated?

Proof -

Let us assume that,

The price of a ticket = x

The revenue = R

Now,

a)

Total number of tickets sold , N = 21000 + 3000(10 - x)

                                                     = 21000 + 30000 - 3000 x

                                                     = 51000 - 3000 x

⇒Total number of tickets sold , N = 51000 - 3000 x

Now,

Revenue , R(x) = x * N

                        = x [ 51000 - 3000 x ]

                        = 51000 x - 3000 x²

⇒R(x) =  51000 x - 3000 x²

b)

For maximum Revenue,

Put \frac{dR(x)}{dx} = 0

Now,

\frac{dR(x)}{dx} = 51000 - 6000 x

⇒51000 - 6000 x = 0

⇒6000 x = 51000

⇒6x = 51

⇒x = \frac{51}{6} = 8.5

∴ we get

When the Revenue is maximum, The price = $ 8.5

c)

If No Revenue is generated

⇒R(x) = 0

⇒51000 x - 3000 x² = 0

⇒1000 x ( 51 - 3 x ) = 0

⇒1000 x = 0, 51 - 3 x = 0

⇒x = 0, 3 x = 51

⇒x = 0, x = \frac{51}{3}

⇒x = 0, x = 17

∴ we get

When No revenue is generated, The price of the ticket is $17

You might be interested in
During 2010, raines umbrella corp. had sales of $850,000. cost of goods sold, administrative and selling expenses, and depreciat
I am Lyosha [343]
To calculate: 
1) Net income (loss) for 2010.
 2) Operating cash flow 
 Solution: 1)
 Sales = $850000
 Less: Cost of goods sold = $610000
  Gross profit = $240000
 Less: Administrative and selling expenses = $110000 
 Earning before Interest, Tax and Depreciation = $130000
 Less: Depreciation = $140000
  Earning before Interest and Tax (EBIT) = ($10000)
 Less: Interest expense = $85000
  Earning before tax (EBT) = ($95000)
 Less: Tax = $0 (as company is having negative EBT or loss hence no tax)

 
 Net loss = $95000  
 2) Operating cash flow 
 EBIT + Depreciation - Tax 
 Wherein, EBIT = Earning before Interest and Tax
  ($10000) + 140000 - 0 = $130000
4 0
3 years ago
Freda is a cash basis taxpayer. In 2019, she negotiated her salary for 2020. Her employer offered to pay her $21,000 per month i
nataly862011 [7]

Answer:

A. N0

B. She may likely bargain for the payments that was reason been that she expects the payments to be in a lower marginal tax bracket in 2021

C. NO

Explanation:

a. No .Based on the information given the amount of $252,000 was NOT constructively received in the year 2020 reason been that She has the amount of $132,000 which is a deferred income amount that

is not constructively received in 2019 and the reason why the amount was not received was because been under the main contract terms she did not have the sole right to receive the income in the year 2020.

b. Freda's willingness to spread her salary over a longer period of time may be due to the fact that She may likely bargain for the payments reason been that she expects the payments to be in a lower marginal tax bracket in the year 2021

c. Based on the information given she is NOT in constructive receipt of the income in the year 2020.

4 0
2 years ago
Suppose the economy is in long-run equilibrium. In a short span of time, there is a decline in the money supply, a tax increase,
Mkey [24]

Answer:

The price level and GDP will fall.

Explanation:

A decline in money supply will increase the interest rate, as a result the investment will decline. This will cause production to decrease. An increase in tax will cause the cost of production to increase, reducing the supply. The taxes will decrease the disposable income, further reduing demand and cnsumption. A pessimistic expectation of business will also cause production to decline.

A rise in the value of dollars will make exports expensive, reducing exports. All of this will cause the GDP and price level to decline.

8 0
2 years ago
In the last few decades the car manufacturing sector has found it difficult to compete with foreign car imports. High labor cost
vladimir2022 [97]

Answer: c. It could allow real wages to downwardly adjust more easily.

Explanation:

When there is modest inflation, companies in the car manufacturing industry can simply decide not to increase nominal wages. This would lead to a fall in real wages as inflation would ensure that the nominal wages are less than they were worth before.

This decrease in real wages will allow the companies in the industry to reduce labor costs in real terms and become more competitive with the foreign manufacturers.

3 0
3 years ago
The key financial consideration in choosing between private and 3pl distribution options is __________________________________.
Anon25 [30]
I believe the answer is D!



Have a Warm and Wonderful Day!!
5 0
3 years ago
Other questions:
  • "The board of directors of Capstone Inc. declared a $0.70 per share cash dividend on its $3 par common stock. On the date of dec
    9·1 answer
  • Under the _____ inventory method, accounting records maintain a continuously updated inventory value.
    13·1 answer
  • Which of the following strategies is illegal in the U.S. and many other countries?
    13·2 answers
  • Sandhill Company reports the following operating results for the month of August: sales $382,500 (units 5,100), variable costs $
    6·1 answer
  • Property rights _________________________________________.
    9·1 answer
  • Departmental contribution to overhead is calculated as revenues of the department less:
    13·1 answer
  • Suppose you have the following values for a short-run production process: Q = 20, VC = 100, FC = 600 and MC = 40. Given this, we
    8·1 answer
  • The Davises pay the annual property tax of $1,825 on their lake house every January. On a whim, they sell the lake house to the
    9·1 answer
  • The amount of money withheld from an employee's paycheck is...
    8·1 answer
  • How long will it take money to double if compounded continuously
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!