A football club is the only one in its region and is therefore able to behave like a monopolist. It sells tickets to Adults (a) and Juniors (j), whose demand curves are given by:
Pa = 200 − Qa
Pj = 160 − Qj
Additionally, the club’s total costs are given by = 20Qi
The club hires an economist to consider its pricing strategy and receives the advice that it should charge different prices to each type of supporter. Find the prices it sets in both markets, the sales (output) in each and its overall level of profit and illustrate profit maximising outputs and prices of each consumer type on a graph (one graph for each type of consumer). Calculate consumer surplus in this case.
Answers
Answer:
Adult market
price: 110sales: 9900profit: 8100consumer surplus: 9000Junior market
price: 90sales: 6300profit: 4900consumer surplus: 5600Total profit: 13000
Total consumer surplus: 14600
Step-by-step explanation:
Given Adult (a) and Junior (j) demand equations Pa = 200 -Qa and Pj = 160 -Qj, and cost equation C = 20Q, you want to find the price in each market that maximizes profit, the sales in each market, and the consumer surplus, and a graph of profit-maximizing sales and prices.
RevenueEach demand equation is of the form P = Pmax -Q, where P is the price that will result in sales of Q tickets. The revenue (R) in each case is the product of numbers of tickets sold (Q) and the price at which they are sold (P).
R = QP = Q(Pmax -Q)
ProfitThe profit is the difference between revenue and cost.
Profit = R - C = Q(Pmax -Q) -20Q
Profit = Q(Pmax -20 -Q)
Writing the demand equation in terms of P, we find ...
Q = Pmax -P
Substituting this into the Profit equation gives ...
Profit = (Pmax -P)(Pmax -20 -(Pmax -P))
Profit = (Pmax -P)(P -20)
The profit function describes a downward-opening parabolic curve with zeros at P=Pmax and P=20. The maximum profit is on the line of symmetry of this curve, halfway between these values of P:
Price for maximum profit = (Pmax +20)/2 = Pmax/2 +10
PricesIn the adult market, Pmax = 200, so the profit-maximizing ticket price is ...
Pa = 200/2 +10 = 110 . . . . price for maximum profit in Adult market
In the Junior market, Pmax = 160, so the profit-maximizing ticket price is ...
Pj = 160/2 +10 = 90 . . . . price for maximum profit in Junior market
SalesUsing the revenue equation, we find the sales in each market to be ...
Qa = 200 -Pa = 200 -110 = 90
Ra = Qa·Pa = 90(110) = 9900 . . . . sales in Adult market
Qj = 160 -Pj = 160 -90 = 70
Rj = Qj·Pj = 70(90) = 6300 . . . . sales in Junior market
Overall ProfitThe profit in each market is ...
Adult market profit = 90(110 -20) = 8100
Junior market profit = 70(90 -20) = 4900
The overall profit will be the sum of the profits in each market:
Overall profit = 8100 +4900 = 13000
Consumer surplusThe consumer surplus in each market is the area below the demand curve and above the price point. It is half the product of the maximum price and the quantity actually sold.
CSa = (1/2)(200)Qa = 100(90) = 9000
CSj = (1/2)(160)(Qj) = 80(70) = 5600
The total consumer surplus is ...
CS = CSa +CSj = 9000 +5600 = 14,600 . . . . total consumer surplus
Graph
The first attachment shows the sales (output) in each market (red=Adult, purple=Junior) as a function of ticket price. It also shows the corresponding profit (orange=Adult, blue=Junior). The profit-maximizing price point is marked on each curve. You will note that it is different from the output-maximizing price point.
The second attachment illustrates the consumer surplus in each market. That graph has price on the vertical axis, and quantity on the horizontal axis. The colors correspond to the colors on the graph in the first attachment.
Related Questions
What is the surface area of the rectangular prism
represented by the net shown?
6 in.
1.5 in.
1.5.in.
Answers
#2
The shape can be cut into four rectangles and two squares.
Total surface area:
⇒ four rectangles + two squares
⇒ 4(Length × Width) + 2(side × side)
⇒ 4(6 × 1.5) + 2(1.5 × 1.5)
⇒ 36 + 4.5
⇒ 40.5 inch²
Therefore, the surface area of the rectangular prism is 40.5 inch²
#3
The polygons that would be used in this net surface area are:
✔ rectangle
✔ square
Answer:
40.5 in²
Step-by-step explanation:
Formula applied :
Surface Area (rectangular prism)
⇒ 2(Length × Width + Width × Height + Length × Height)
=============================================================
Given :
⇒ Length = 6 inches
⇒ Width = 1.5 inches
⇒ Height = 1.5 inches
============================================================
Solving :
⇒ Surface Area = 2(6 × 1.5 + 1.5 × 1.5 + 6 × 1.5)
⇒ Surface Area = 2(9 + 2.25 + 9)
⇒ Surface Area = 2 × 20.25
⇒ Surface Area = 40.5 in²
200 people are asked about three brands of beverages Coffee, Tea and Chocolate. 36 like
Coffee only, 46 like Coffee but not Tea, 52 like Coffee, 16 like Tea and Chocolate, 96 like
Chocolate, 16 like Coffee and Chocolate while a total of 108 like one and only one of the
beverages.
Required
i) Calculate the number of people like black coffee?
ii) How many people don’t like any of the drinks?
Answers
Answer:
32
Step-by-step explanation:
Answer:
i) 52
ii) 66
Step-by-step explanation:
This sort of problem is usually solved using some sort of table or Venn diagram. We have used a table in the attachment such that each of the cells in the grid represents one of the 8 possible combinations of coffee, tea, or chocolate.
The numbers in black are given directly by the problem statement. The numbers in blue are calculated from the numbers in black and one of the other given numbers in the problem statement. The numbers in red are calculated so the totals work out correctly.
The cells shaded blue-gray are "one and only one" of the drinks. The cell shaded purple-gray is "don't like any".
__
i) black coffeeWe assume that any form of "coffee" is "black coffee." The problem statement tells us 52 people like coffee.
__
ii) noneThe last number we calculated is the number who like none of the drinks: 66. This brings the total of non-coffee drinkers to 148.
_____
Additional comment
As noted above, the colors more or less indicate the order of the calculations. We started with 36 who like coffee only, and 46 who like coffee and not tea. That means 46-36=10 like coffee and chocolate, but not tea.
Since 16 like coffee and chocolate, that leaves 16-10=6 who like coffee and tea and chocolate (all three).
96 like chocolate, but 16 of those like chocolate and tea. The other 80 like chocolate, but not tea.
46+16=52, so there must be 0 who like coffee and tea, but not chocolate.
The number who like only one is 108. We already have 36 that are coffee only, 80-10 = 70 that are chocolate only, so there must be 108 -70 -36 = 2 who like tea only.
Now, we can finish filling the top row of the table and the totals in the bottom row.
Determine the value of y.
135°
27°
24°
45°
Answers
Find the area of a regular polygon with 7 sides that has a perimeter of 63 inches and an apothem of 8 inches.
Area = [?]in2
Answers
Answer:
see the attachment photo!
Given that the line y=ax+b passes through the points A(0; 3) and B(-2;7), how do I find the values of a and b?
Answers
To compute the slope, you simply have to find the difference of y coordinates and divide them by the difference of x coordinates:
a = (y2-y1)/(x2-x1)
a = (7-3)/(-2–0)
a = 4/-2
a = -2
To compute the y intercept denoted by b, we substitute the value of a with -2 in the formula and choose any point (x,y) and substitute their values in the formula as well. Like so:
I choose point A:
3 = (-2)(0) + b
3 = b
11 12 13
18
A local charity holds a carnival to raise money. In one
activity, participants make a $3 donation for a chance
to spin a wheel that has 10 spaces with the values, 0,
1, 2, 5, and 10. Whatever space it lands on, the
participant wins that value. Let X represent the value of
a random spin. The distribution is given in the table.
Value of a Spin
0
1
2
5
10
Probability
0.4 0.2
0.2
0.1
0.1
20
Which of the following is the correct interpretation of
P(X<5)?
Answers
The correct interpretation of the probability P(X < 5) is; 0.8
How to Solve Probability?We are given the probability of the spin values are;
Probability of Spin Value of 0 = 0.4
Probability of Spin Value of 1 = 0.2
Probability of Spin Value of 2 = 0.2
Probability of Spin Value of 5 = 0.1
Probability of Spin Value of 10 = 0.1
P(X < 5) simply means the probability of getting a spin value less than 5. Thus;
P(X < 5) = P(0) + P(1) + P(2)
P(X < 5) = 0.4 + 0.2 + 0.2
P(X < 5) = 0.8
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Which of the following equations is equivalent to S=pi r^2 h
Answers
The equation that is equivalent to S=pi r^2 h is h = S/pir^2
Subject of formulaThis is a way of representing a variable with another. Given the equation
S=pi r^2 h
We are to make 'h" the subject of the formula.
Divide both sides by pir^2
S/pir^2 =pi r^2 h/pir^2
h = S/pir^2
Hence the equation that is equivalent to S=pi r^2 h is h = S/pir^2
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A graph shows the number of texts, numbered 10 to 100, on the x-axis, and the total cost in dollars, numbered 3 to 27, on the y-axis. A straight red line with a positive slope, labeled Emilia, begins at (0, 10), and a straight blue line with a positive slope, labeled Hiroto, begins at (0, 20). Both lines intersect at point (50, 22.5).
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.
Both plans cost the same when 22 texts are sent.
Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
Both plans cost the same when 50 texts are sen
Answers
Answer: Both plans cost the same when 50 texts are sent.
Step-by-step explanation:
When x=50 (meaning 50 texts are sent), the y coordinate (which represents the cost) is the same.
Reese, Greg, and Brad meet once a week for coffee. They each have their favorite café and, to be fair, they use
randomization to choose where they will meet. Each person has a colored marble: red (R) for Reese, green (G) for
Greg, and blue (B) for Brad. Each week, all three marbles are mixed well in a bag and a marble is selected. The
favorite café of the person associated with the selected marble is chosen for that week's meeting. Which of the
following represents the sample space for choosing a café for the first two weeks?
OR & G, R & B, G & R, G & B, B &R, B & G
OR&R, R&G, R & B, G & G, G & B, B & B
R&R, R&G, R & B, G & R, G & G, G & B, B &R, B&G, B & B
R&R, R&G, R & B, R & G, G&R, G & G, G & B, B &R, B & G, B & B
OO
Answers
All the samples are given as {R&R, R&G, R&B, G&R, G&G, G&B, B&R, B&G, B&B}.
What are sample?A sample is a group of clearly specified components. The number of items in a finite sample is denoted by a curly bracket.
Reese, Greg, and Brad meet once a week for coffee.
They each have their favorite café and, to be fair, they use randomization to choose where they will meet.
Each person has a colored marble: red (R) for Reese, green (G) for Greg, and blue (B) for Brad.
Each week, all three marbles are mixed well in a bag and a marble is selected.
The favorite café of the person associated with the selected marble is selected for that week's meeting.
Then the total number of the outcomes will be
Total outcomes = 3 × 3
Total outcomes = 9
All the samples are given below.
{R&R, R&G, R&B, G&R, G&G, G&B, B&R, B&G, B&B}
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He was, without a doubt, the most prolific writer of mathematics of all time. Euler is credited as being the first mathematician to define function in the way we currently think of functions. In his book, Introductio in analysin infinitoriumin, he stated, “A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”
Based on what we know a function to be today, what did Euler mean by an analytic expression?
an expression formed with many variables and no numbers
an expression formed with many numbers and no variables
an expression formed from operations such as addition, multiplication, powers, and roots
an expression formed using only multiplication of a variable and a number
Answers
Based on what we know a function to be today, Euler mean an analytic expression "an expression formed from operations such as addition, multiplication, powers, and roots"
Euler's definition of a functionAccording to Euler, a function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”
The function is. combination of expression which includes variables and constants using various operations such as roots, power and multiplication.
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need help with this math
Answers
Answer:
x = -12
y = 10
(x, y) = (-12, 10)
Step-by-step explanation:
the perpendicular distance of a point from the x-axis is 4 units and the perpendicular distance from the y axis is 5 units write the coordinates of such a point if it lies in the first quadrant second quadrant third quadrant and fourth quadrant
Answers
Step-by-step explanation:
let p be the point which is at a distance of 4 units from the x-axis and at a distance of 5 units from the y axis
(i) When P lies in the first quadrant then the coordinates of P are (5,4).
(ii) When of P lies in the second quadrant then the coordinates of P are (-5,4).
(iii) When P lies in the third quadrant then the coordinates of P are (-5,-4).
(iv) When P lies in the fourth quadrant then the coordinates of P are (5,-4).
Hope it helps you!!Known as periodic reports, interim reports or interim statements, these updates provide important company information between annual reporting periods. To help protect investors and keep the public informed, regulations typically require public companies to submit company performance reports more than once a year.Known as periodic reports, interim reports or interim statements, these updates provide important company information between annual reporting periods. To help protect investors and keep the public informed, regulations typically require public companies to submit company performance reports more than once a year.
Design an instructional activity that could help learners recognise that decimal
fractions can be applied across environmental situations (relating to activities
in real life).
Answers
Fraction refers to a part of a whole; e.g when cup is not completely filled, it covers only a part of the cup
What is fraction?The term fraction refers to a part of a whole. To design an instructional activity that could help learners recognize that decimal fractions can be applied across environmental situations, we could look at certain things in the house.
For instance, when cup is not completely filled, it contains water that covers only an fraction of the cup. Also, we could boil a part and not a whole cup of rice. These are all examples of fractions.
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Two lines are intersecting. What is the value of x?
Answers
Answer:
The correct answer is x = 51.
Step-by-step explanation:
We have been given an image of two intersecting lines. We are asked to find the value of x.
We can see that both angles are supplementary (adding up to 180 degrees), so we can set an equation as:
x + 23 + 2x + 4 = 180
x + 2x + 4 + 23 = 180
3x + 27 = 180
3x + 27 - 27 + 180 - 27
3x = 153
3x/3 = 153/3
x = 51
Therefore, the value of x is 51.
Hope this helps:) Goodluck!
Answer:
Step-by-step explanation:
2x + 4 + x + 23 = 180
3x + 27 = 180
3x = 153
x = 51
Please help me with my math
Answers
There are 5 new books and 6 used books on a shelf. (a) What is the ratio of used books to all books on the shelf?
Answers
If there are 6 used books and 11 total books, then there are 6 used books per 11 total books hence 6:11
The load requirement in your plan is 60 psf at a joist spacing of 16 inches . If the room dimensions are length 13 feet 2 inches and width 11feet 7 inches are 2 by 10 boards appropriate
Answers
The correct answer is; No, because the 2 x 10 boards can support neither the width nor length of the room.
How to find the dimensions?
We are given;
Load requirement = 60 psf
Joist Spacing = 16 inches
Length of room; 13 feet 2 inches
Width of room; 11 feet 7 inches.
Since we want to consider whether 2 by 10 boards are appropriate, this length of 2 by 10 will not be appropriate because it cannot cover up for a room with dimensions of 13 feet 2 inches and 11 feet 7 inches.
Thus, we can conclude that No, because the 2 x 10 boards can support neither the width nor length of the room.
The missing options are;
A. Yes, because 2 x 10 boards can support the width and length of the room
B. Yes, because 2 x 10 boards support the 70 psf
C. No, because 2 x 10 boards can support only the width of the room
D. No, because the 2 x 10 boards can support neither the width nor length of the room
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please I need the answer
Answers
Answer:
The answer is c
Step-by-step explanation:
one add the numbers 108 & 96=204
then add the numbers from c which is 30+30=60 43+43=86 29+29=58
then add 60+86+58 which will be 204 so c is the answer your welcome
come
A candidate for office plans to visit 6 cities before the state primary.
How many different ways can the campaign staff arrange her travel route?
Enter your answer as a whole number, like this: 42
Question 2
A candidate for office plans to visit 6 cities before the state primary.
How many different ways can the campaign staff arrange her travel route?
Enter your answer as a whole number, like this: 42
Answers
There are 720 different ways the campaign staff can arrange her travel route
How to determine the number of route?The given parameter is:
Cities = 6
The candidate cannot be at all 6 cities at the same time.
This means that we make use of factorial.
So, we have:
Ways = 6!
Evaluate the factorial expression
Ways = 720
Hence, there are 720 different ways the campaign staff can arrange her travel route
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9 cm
6 cm
8 cm
12. Some high school students made a rectangular prism-shaped box, shown in the figure, to
will be available. Find the volume of the rectangular prism.
OA. 432 cm³
O B. 348 cm³
O C. 729 cm³
O D. 512 cm³
O Mark for review (Will be highlighted on the review page)
Answers
Answer:
A
Step-by-step explanation:
the answer is A because I said its C :)
A recipe for trail mix calls for 234
2
3
4
cups of peanuts, 123
1
2
3
cups of cashews, and 116
1
1
6
cups of almonds.
How many cups of nuts are used in all?
Answers
Please please help please please help me please please help please please help me please please help please please help me please please help please please help me please please help please please help me please
Answers
Answer: 2+2= DA ROCK
Step-by-step explanation:
SCAM..... ITS ABOUT DRIVE ITS ABOUT POWER WE STAY HUNGRY WE DEVOURE PUT IN THE WORK PUT IN THE HOUR AND TAKE WHATS OURSSSSSSSSSSSSSSSSSSSSS
YEHHHHHHHH
What is the future value of a 5-year annuity due with annual payments of $ 2,535 , evaluated at a 14.18 percent interest rate? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.
Answers
Answer:
$19,201.09
Step-by-step explanation:
The future value of the annuity due can be found using any of a number of apps, calculators, or spreadsheets. It can also be found using the formula ...
A = P(1 +r)((1 +r)^n -1)/r
where P is the annual payment, r is the annual interest rate, and compounding is yearly for n years.
A = 2535(1.1418)(1.1418^5 -1)/0.1418 ≈ 19,201.09
The value will be $19,201.09.
Find the side of an equialateral triangle if it's area is 9√3 cm2
Answers
Step-by-step explanation:
We know that the area of an equilateral triangle of side a cm is
[tex] \rm \: Equilateral \: Triangle = \cfrac{ \sqrt{3} }{4} {a}^{2} \: cm[/tex]Let a cm here be 9√3 then we could get our solution.
[tex] \rm\implies \rm 9 \sqrt{3} = \cfrac{ \sqrt{3} }{4} \: a {}^{2} [/tex]
[tex] \implies \rm \: \cfrac{ \sqrt{3} }{4} {a}^{2} = 9 \sqrt{3} [/tex]
[tex] \implies \rm \: a {}^{2} = 36[/tex]
[tex] \implies \rm \: a = \sqrt{36} = \sqrt{6 \times 6} [/tex]
[tex] \implies \rm \: a = 6 \: cm[/tex]
Thus, the side of the equilateral triangle is 6 cm.
Jen wants to save money for the future. Jen invests $1,100 in an account that pays interest rate of 4%.
How many years will it take for the account to reach $2,900? Round your answer to the nearest hundredth.
Answers
The number of years it will take for the money to be $2900 is 40.91 years
How to find the years the money will accrue to 2900 dollars?Using simple interest formula,
I = prt / 100
we are looking for t
where
p = principalr = ratet = timeI = simple interestTherefore,
I = 2900 - 1100 = 1800
1800 = 1100 × 4 × t / 100
cross multiply
180000 = 4400t
t = 180000 / 4400
t = 40.9090909091
t = 40.91 years
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The radius of a semicircle is 5 centimetres. What is the semicircle's diameter?
Answers
The diameter [tex]d = 2r[/tex], where [tex]r[/tex] is the radius. Thus, [tex]d = 2 \times r = 2 \times 5 = 10cm[/tex]
If a multiple-choice test consists of 5 questions, each with 4 possible answers of which only 1 is correct, (a) in how many different ways can a student check off one answer to each question?
(b) in how many ways can a student check off one answer to each question and get all the answers wrong?
Answers
Answer:
(a) 1024 ways
(b) 243 ways
Step-by-step explanation:
When answers are independent, the total number of ways all questions can be answered is the product of the number of ways each question can be answered.
__
(a)The first question can have one answer 4 ways. The second question can be answered 4 ways for each of the ways the first question was answered. That is, the two questions can be answered 4×4 = 16 ways. Similarly, each additional question multiplies the number of ways the questions can be answered by 4.
The 5 questions can be answered 4×4×4×4×4 = 4^5 = 1024 ways.
__
(b)There are 3 ways to answer the first question incorrectly. Each additional question can be answered incorrectly 3 ways for each of the ways previous questions were answered. The total number of ways all questions can be answered incorrectly is ...
3^5 = 243
A student can answer all questions wrong in 243 different ways.
Find the value of x.
33°
107°
x
Answers
Answer:
140
Step-by-step explanation:
Angles in a triangle add up 180 :
180 = 107 + 33 + y
y = 180 - (107+33)
y = 180 - 140
y = 40
Angles on a straight line add up to 180 so :
180 = x + y
180 = x + 40
x= 180 - 40
x = 140
Hope this helped and have a good day
Answer:
x = 140°
Step-by-step explanation:
Concepts
The Exterior Angle Theorem states that the two remote angles in a triangle is equal to the exterior angle.
Application
In this case, the two remotes angles are 107 and 33°, and the exterior angle is x. Now, all we have to do is just add 107 and 33 to get our answer.
Solution
107 + 33140°What is the length of a diagonal of a square with a side length of 8?
A. 4
B. 42
C. 4√3
D. 8√√2
Answers
Living on less than what you make means not
Answers
Answer:
living beyond your means.
Step-by-step explanation:
Pay for what you need and don't go into debt.