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
ANTONII [103]
3 years ago
9

Before the pandemic cancelled sports, a baseball team played home games in a stadium that holds up to 50,000 spectators. When ti

cket prices were set at $12, the average attendance was 30,000. When the ticket prices were on sale for $10, the average attendance was 35,000.
(a) Let D(x) represent the number of people that will buy tickets when they are priced at x dollars per ticket. If D(x) is a linear function, use the information above to find a formula for D(x). Show your work!
(b) The revenue generated by selling tickets for a baseball game at x dollars per ticket is given by R(x) = x-D(x). Write down a formula for R(x).
(c) Next, locate any critical values for R(x). Show your work!
(d) If the possible range of ticket prices (in dollars) is given by the interval [1,24], use the Closed Interval Method from Section 4.1 to determine the ticket price that will maximize revenue. Show your work!
Optimal ticket price:__________ Maximum Revenue:___________
Mathematics
1 answer:
spayn [35]3 years ago
3 0

Answer:

(a)D(x)=-2,500x+60,000

(b)R(x)=60,000x-2500x^2

(c) x=12

(d)Optimal ticket price: $12

Maximum Revenue:$360,000

Step-by-step explanation:

The stadium holds up to 50,000 spectators.

When ticket prices were set at $12, the average attendance was 30,000.

When the ticket prices were on sale for $10, the average attendance was 35,000.

(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)

Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).

\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500

Therefore, we have:

y=-2500x+b

At point (12,30000)

30000=-2500(12)+b\\b=30000+30000\\b=60000

Therefore:

D(x)=-2,500x+60,000

(b)Revenue

R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2

(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.

R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12

The critical value of R(x) is x=12.

(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]

Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.

R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0

Therefore:

  • Optimal ticket price:$12
  • Maximum Revenue:$360,000

You might be interested in
Someone please explain how to get the answer and what the answer is thank you
Natalka [10]
The volume of a cylinder is

V=hpr^2 in this case h=40, r=20/2=10, and we will approximate pi as 3.14 so:

V=40(3.14)(10^2)

V=12560 ft^3
7 0
3 years ago
I need help with number 11. Can someone please help me.
noname [10]

Answer:

9

Step-by-step explanation:


8 0
3 years ago
Which is a solution to the equation y = 5x + 1
bija089 [108]

Answer:

(5,26)

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
PLEASE ASAP! I will give brainliest!!
Kay [80]

Answer:

Yes

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
I WILL GIVE BRAINLIEST The fuel efficiency of Natalie's car is 25 miles per gallon. Which of the following statements are true?
sleet_krkn [62]

Answer:

The fuel efficiency of Natalie's car is 25 miles per gallon. Which of the following statements are true? Select two that apply.

a. For every mile Natalie travels, she uses 25 gallons.

b. For every gallon Natalie uses, she travels 0.04 miles.

✓c. <u>For every mile Natalie travels, she uses 0.04 gallons.</u>

✓d. <u>For every gallon Natalie uses, she travels 25 miles.</u>

C. and D. are the right answer.

8 0
2 years ago
Other questions:
  • Identify the constant term in this expression. 28m + 4n − 12m + 3
    7·2 answers
  • What is the mode for the data set?
    8·2 answers
  • Could -2 be used to rewrite 32
    12·2 answers
  • Graph the line with slope <br> 2<br> 5<br><br> and <br> y<br><br> -intercept <br> −<br> 7<br><br> .
    11·1 answer
  • Among 21- to 25-year-olds, 29% say they have driven while under the influence of alcohol. Suppose that three 21- to 25-year-olds
    15·1 answer
  • The Jones family is driving from San Antonio, Texas, to Anchorage, Alaska, which is a distance of 4304 miles. They have already
    8·1 answer
  • Need help with my final it’s my final grade
    10·1 answer
  • 110 percent of 90 is what number
    15·2 answers
  • How many unit cubes are needed to make the large cube?
    11·1 answer
  • The value of y is directly proportional to x.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!