g A gift shop sells 40 wind chimes per month at $110 each. The owners estimate that for each $11 increase in price, they will sell 2 fewer wind chimes per month. Find the price per wind chime that will maximize revenue.

Answers

Answer 1

Answer:

The price that maximizes the revenue is $165

Step-by-step explanation:

We can model the price as a function of sold units as a linear relationship.

Remember that a linear relationship is something like:

y = a*x + b

where a is the slope and b is the y-intercept.

We know that if the line passes through the points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

For this line, we have the point (40, $110)

which means that to sell 40 units, the price must be $110

And we know that if the price increases by $11, then he will sell 2 units less.

Then we also have the point (38, $121)

So we know that our line passes through the points (40, $110) and  (38, $121)

Then the slope of the line is:

a = ($121 - $110)/(38 - 40) = $11/-2 = -$5.5

Then the equation of the line is:

p(x) = -$5.5*x + b

to find the value of b, we can use the point (40, $110)

This means that when x = 40, the price is $110

then:

p(40) = $110 = -$5.5*40 + b

            $110 = -$220 + b

       $110 + $220 = b

        $330 = b

Then the price equation is:

p(x) = -$5.5*x + $330

Now we want to find the maximum revenue.

The revenue for selling x items, each at the price p(x), is:

revenue = x*p(x)

replacing the p(x) by the equation we get:

revenue = x*(-$5.5*x + $330)

revenue = -$5.5*x^2 + $330*x

Now we want to find the x-value for the maximum revenue.

You can see that the revenue equation is a quadratic equation with a negative leading coefficient. This means that the maximum is at the vertex.

And remember that for a quadratic equation like:

y = a*x^2 + b*x + c

the x-value of the vertex is:

x = -b/2a

Then for our equation:

revenue = -$5.5*x^2 + $330*x

the x-vale of the vertex will be:

x = -$330/(2*-$5.5) = 30

x = 30

This means that the revenue is maximized when we sell 30 units.

And the price is p(x) evaluated in x = 30

p(30) = -$5.5*30 + $330 = $165

The price that maximizes the revenue is $165


Related Questions

If a batch of cookies uses
2
2
3
cups of sugar, then how much sugar is needed to make 5 batches of cookies

Answers

Answer:

13 1/3 cups of sugar

Step-by-step explanation:

Which of the following can be used to represent the complement of event X?

Answers

2nd X..

I hope that this is correct

LESSON 3
WHATS MORE
Translate each English phrase/sentance into Mathematical phrase/sentance
1. The sum of 4 and number________
2. Six less than a number_________
3. The product of 8 and a number______
4. The quotient of x and 7 ______
5. Five more than a number is equal to 15_____ ​

Answers

Answer:

1. 4+x

2. x-6

3. 8x

4. x/7

5. x+5=15

Step-by-step explanation:

Figure F is a scaled copy of E.

What is length of each missing measurement.

Answers

Answer:

answer

Step-by-step explanation:

what are do u mean what is f and e explain properly and then people will tell u

5. Seismologists use the Richter scale to measure the magnitudes and intensity of
earthquakes that occur all over the earth. (see below, some info about Richter scales,
and intensity formula)
Let's say an earthquake hit Santa Monica, CA and had a magnitude of 6.2. If another
earthquake hit Charleston, SC and was a magnitude of 3.8, then how much more
intense was the earthquake in LA?
Student's Work
Student's Answer
A. 251.19 times
B. 11.02 times
C. 42.81 times
D. 2.4 times
Some additional Richter scale info...
A common logarithm is a logarithm with base 10. You can write a common logarithm logio * simply as log x, without
showing the 10
Many measurements of physical phenomena have such a wide range of values that the reported measurements are
logarithms (exponents) of the values, not the values themselves. When you use the logarithm of a quantity instead of the
quantity, you are using a logarithmic scale. The Richter scale is a logarithmic scale. It gives logarithmic measurements
of earthquake magnitudo.
1
3) 1 Hot 10
Intensity formula:
-
= M - M₂
-
log
12

Answers

Applying logarithms, it is found that the earthquake in LA was 251.19 times more intense, and the correct option is A.

The logarithm of the ratio of intensity of two earthquakes of magnitudes [tex]M_1[/tex] and [tex]M_2[/tex] is given by:

[tex]\log{\frac{I_1}{I_2}} = M_1 - M_2[/tex]

[tex]\frac{I_1}{I_2}[/tex] gives how much more intense earthquake 1 is compared to earthquake 2.

In this problem, [tex]M_1 = 6.2, M_2 = 3.8[/tex], then:

[tex]\log{\frac{I_1}{I_2}} = M_1 - M_2[/tex]

[tex]\log{\frac{I_1}{I_2}} = 6.2 - 3.8[/tex]

[tex]\log{\frac{I_1}{I_2}} = 2.4[/tex]

[tex]10^{\log{\frac{I_1}{I_2}}} = 10^{2.4}[/tex]

[tex]\frac{I_1}{I_2} = 251.19[/tex]

Hence, the earthquake in LA was 251.19 times more intense, and the correct option is A.

A similar problem is given at https://brainly.com/question/2528611

A pipe that is 165 feet long is cut into three parts whose lengths are in the ratio 2 : 5 : 8. Find the length of the longest piece. Longest piece: 2 feet

Answers

Answer:

88 ft

Step-by-step explanation:

Let's say the shortest piece has length 2x, so the medium piece has length 5x and the longest piece has length 8x. Added together, they equal 165, so

2x + 5x + 8x = 165

15x = 165

divide both sides by 15 to isolate x

x = 11

8x = longest piece = 88 ft

What is the sum of the 1st square number and the 4th cube
. Number

Answers

Answer: there is nothing here with the info i need 2 anwser this question srry.

Step-by-step explanation:

Answer:

i think it is 65

Step-by-step explanation:

the 4th cube number is 64 and the first square number is 1 64+1=65

however if you use the first square number as 4 then it is 68

A rectangle’s perimeter is 86in . Its length is 9in longer than its width. Use an equation to find the rectangle’s length and width.

Answers

Answer:

Step-by-step explanation:

Let width be x

So length would be x + 9

If perimeter is 86, then

2(l+b) = 86

2(x + x+9) = 86

4x + 18 = 86

4x = 68

X = 17

Check:

2(x + x + 9) = 86

2(17 + 17 + 9) = 86

2(43) = 86

86 = 86

Here you go

8. Paula needs to replace the floor in her family room since her cat peed in several
places. She wants to put down both vinyl flooring and carpet in the room. The
carpet she selected costs $2 per square foot. The vinyl floor covering costs $1
per square foot. She has $500 to spend on materials and must cover an area of
300 square feet. How much carpet and vinyl flooring will she buy to meet her
requirements?

Answers

So Looks like it’s area so 2x1x500x300 =300000

The chart shows the sizes and prices of different sized boxes of Alex's favorite cereal.

Answers

Step-by-step explanation:

Compare the rates

Whichever has the smaller rate is the best deal.

remember, to be able to compare both cereal boxes they must have the same unit of measure (grams with grams, ounces with ounces, etc.)

Answer:

Price of box of cereal #1

---------------------------- = $ per ounce(or other unit)

Size of box #1 (in ounces,

or some other unit)

PLS HELP ME WITH THIS (4 x 1) + (4 x 3)

Answers

Answer:

16

Step-by-step explanation:

4x1 is 4

4x3 is 12

4+12 is 16

Answer:

16

Step-by-step explanation:

In the art club, there are 2 seventh graders for every 3 eighth graders. At
this year's art fair, there were 7 paintings by seventh graders for every 12
paintings by eighth graders. Is the ratio of seventh graders to eighth
graders in the art club equivalent to the ratio of paintings by seventh
graders to paintings by eighth graders? *

Answers

Answer:

no

Step-by-step explanation:

2/3 does not equal 7/12.

there would need to be 8 paintings by seventh graders for every 12 by eighth graders in order to have an equivalent ratio.

solve for X:
10( x + 1) = 2 x-7
-1
-3
-17/8
-18/8

Answers

-17/8

Step-by-step explanation:

10( x + 1) = 2 x-7

10x + 10 = 2x - 7

10 + 7 = 2x - 10x

17 = - 8x

x = -17 /8

Answer:

Hiya There....!!!

______________________

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x  =  − 17 /18

Decimal Form:

x  =  − 2.125

Mixed Number Form:

x  =  − 2/ 1 8

_______________________

“To forgive is wisdom, to forget is genius. And easier. Because it's true. It's a new world every heart beat.”

― Joyce Cary, The Horse's Mouth

__________________________

Think of life as a mytery because well it sort of is! You don't know what may happen may be good or bad but be a little curious and get ready for whatever comes your way!! ~Ashlynn

pls solve this equation for brainliest 2a+2=8?​

Answers

Answer:

a=3

Step-by-step explanation:

you subtract 2 from both sides of the equation you simplify it and then you divide both sides of the equation by the same term and then simplify it again

Answer:

a=3

Step-by-step explanation:

Find the length of the third side. If necessary, round to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

a² + b² = c²

12² + b² = 15²

b² = 225 - 144

b² = 81

b = 9

A hardware store mixed 7 gallons of red paint with every 11 gallons of blue paint to make purple paint. Which ratio of gallons of red paint to gallons of blue paint will make the same shade of purple paint?

Answers

Answer:

2 b + 6 r = 2 * 24

5 b + 3 r = 2 * 21 ... 10 b + 6 r = 84

subtracting equations (to eliminate r) ... 8 b = 36

solve for b , then substitute back to find r

i need help with number 5

Answers

B : 3x-5

You can find this by solving the first equation for y, you do this by adding y and subtracting 5.

Hope this helps!!

It takes 4/5 of an hour to fill 1/2 tank.how many tanks can she fill in an hour

Answers

Answer:

5/8 of a tank

Step-by-step explanation:

Divide 1/2 by 4 to get how much of a tank you would be able to fill in 1/5 of an hour.  1/2 ⁒ 4 is 1/8 so she can fill 1/2+1/8 of a tank or 5/8 of a tank.

Helppppp please quick

Answers

Answer:

a≥11

Step-by-step explanation:

Because the graph is 11 the minimum and there is no maximum, you can say that a can be equal to 11, or it can also be bigger than 11.

Use the distributive property to multiply 4,345 x 2

Answers

Answer:

8690

Step-by-step explanation:

there is no distributive property just multiply using a regular calculator

What is 26% as a fraction in simplest form?
A. 26/100
B. 26/10
C. 6/25
D. 13/50

Answers

Answer:

it'd be d: 13/50 !!

Answer:

D. 13/50

Step-by-step explanation:

0.26 ⇔ 26/100 ⇔ 13/50

whats .8421 rounded to the nearest tenth

Answers

0.8/0.80
Place value
U I T I H
0 . 8 0

Answer:

8420

weeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

A cube has a surface area of 54cm^2 Find the side length, x, of the cube

Answers

we know that the area of a cube is its side cubed

So, x^3 = 54(i think it should be 64)

x = 4 (if it is 64)

if it is 54 then we will take the cube root of 54

Answer:

3

Step-by-step explanation:

6a^2=54

a^2=54/6

a=root 9

a=3

\displaystyle\lim_{ x \rightarrow 0 } \left( \dfrac{ \sqrt[ m ]{ 1+αx \phantom{\tiny{!}}} \times \sqrt[ n ]{ 1+βx \phantom{\tiny{!}}} -1 }{ x } \right)

Answers

Answer:

What are you trying to ask.

Step-by-step explanation:

Please Write in a understandable  manner.

Thanks from India.

Express as a single power.

Answers

[tex]\\(a)\\2^3 \times 2^6 \div 2^9 = 2^{3+6} \times \dfrac{1}{2^9} = 2^9 \times 2^{-9} = 2^{9-9} = 2^0 = 1\\\\ \\(b)\\\\(-5)^8 \div (-5)^4 \times (-5)^3\\ \\= (-5)^8 \times \dfrac 1{(-5)^4 \times (-5)^3} \\\\= (-5)^8 \times \dfrac{1}{(-5)^{4+3}} \\\\= (-5)^8 \times \dfrac{1}{(-5)^7} \\\\= (-5)^{8 - 7} \\\\=(-5)^1 \\\\ =-5\\\\\\(c)\\\\\\\dfrac{6^3 \times 6^5}{6^2 \times 6^4}= \dfrac{6^{3+5}}{6^{2+4}}= \dfrac{6^8}{6^6}=6^{8-6}=6^2 =36[/tex]

Simplify the product.
(16+13)(12-2)

Answers

Answer:

290

Step-by-step explanation:

(16+13)(12-2)= 29 * 10 = 290

Answer:

290

Step-by-step explanation:

(16+13)(12-2)

29*10

290

Someone help me click this solve it using < or >

Answers

Answer:

<

<

>

Step-by-step explanation:

To compare fractions, we need to make sure that both fractions have the same denominator. For example, for question 4, the least common multiple of 5 and 3 is 15, so we need to multiply both fractions by some numbers to get the denominators equal to 15. In this case, we will multiply the first fraction, [tex]\frac{3}{5}[/tex] by 3 to get [tex]\frac{9}{15}[/tex] and the second fraction, [tex]\frac{3}{3}[/tex] by 5 to get [tex]\frac{15}{15}[/tex].

Once we have the same denominator, we can simply compare the value of the numerators and see which one is larger. For question 4, since 9 is smaller than 15, the first fraction is smaller than the second. So the correct inequality to represent this would be "<".

To do these sums, we have to first convert them to like fractions.

For the first one:

LCM of denominators 5 and 3 is 15.[tex] \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} [/tex][tex] \frac{3}{3} = \frac{3 \times 5}{3 \times 5} = \frac{15}{15} [/tex]Since,[tex] \frac{9}{15} < \frac{15}{15} [/tex]Therefore,[tex] \frac{3}{5} < \frac{3}{3} [/tex]

For the second sum:

LCM of denominators 6 and 8 is 24.[tex] \frac{4}{6} = \frac{4 \times 4}{6 \times 4} = \frac{16}{24} [/tex][tex] \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} [/tex]Since[tex] \frac{16}{24} < \frac{21}{24} [/tex]Therefore,[tex] \frac{4}{6} < \frac{7}{8} [/tex]

For the third one:

LCM of denominators 10 and 5 is 10.[tex] \frac{6}{10} = \frac{6 \times 1}{10 \times 1} = \frac{6}{10} [/tex][tex] \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} [/tex]Since,[tex] \frac{6}{10} > \frac{4}{10} [/tex]Therefore,[tex] \frac{6}{10} > \frac{2}{5} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Given that y = 11 cm and θ = 34°, work out x rounded to 1 DP.

Answers

Check the picture below.

a torist walks 10.5 inches in 3 seconds. how far does it walk per second​

Answers

Divide distance by time:

10.5 inches / 3 seconds = 3.5 inches per second

Answer: 3.5 inches per second

Answer: 31.5

Step-by-step explanation: you multiply the inches by the second.

Add and simplify:
3 + 1
10 5​

Answers

Answer:

I don't under stand the question can u write more clearly

Other Questions
sn xut hng ha da trn nWhich is one method for detecting cancer? Please help me with this on the picture Help.. what does Y= All changes savedGeorgia was preparing an oral report about changes in attitudes toward nutrition over the past century. Georgia interviewed and recorded a nutritionistabout the importance of a healthy diet for athletic and academic performance, and she included an excerpt from the recording in her presentation. Whattype of information did Georgia include?researched factstatisticsan anecdoteO expert opinion What event occurred from 1861-1865A. Revolutionary War B. Battle of Bunker HillC. Civil war D. World War I Which of the following is NOT true of ancient Greek Culture?The formative influence of the Homeric epics in shaping Greek culture and as the beginning of the Western canon of literature are widely recognized by scholars.Socrates was a philosopher and the author of numerous dialogues and letters known for a probing question-and-answer style of examination.Greek tragedy is an extension of the ancient rites carried out in honor of Dionysus; it heavily influenced the theater of ancient Rome and the Renaissance.Aristotle was the tutor of Alexander the Great, founder of the Lyceum and the Peripatetic School of philosophy in Athens.None of the Above Select the next item in the sequence.10.172,10.983,10.994...A. 10.972B. 11.000C.11.172D.11.983 Maria Stewart, abolitionist and former enslaved person, believed what most harmed enslaved people was lack ofself-esteem.education.identity.family. Which of the following is a mineral a.pantothenic acid b.biotinc.folated.magnesium NEED HELP BEFORE I FAIL PLS :( ITS PYTHAGOREAN THEOREM Convert 37.5% to a fraction. (Reduce your answer to lowest terms.) PLEASE ANSWER AS SOON AS POSSIBLEThe trinomial x4x+4 is a perfect square. By factoring and finding the square roots, what values of x make the equation x24x+4=1 true? can anyone pls pls help me! why is the Dna molecule able to open up and close? Production possibilities curve graph PLEASE HELP ASAP!!! I dont understand Conoly Co. has identified an investment project with the following cash flows. If the discount rate is 10 percent, what is the present value of these cash flows? What is the present value at 18 percent and at 24 percent? Year 1, 2, 3, and 4 Cash Flow $1,200, 600, 855 and 1,480 respectively In India, secularism has now been pronounced by the Supreme Court of India to be a part of the basic structure of the Constitution and cannot be done away with even by a constitutional amendment.[9] Articles 25 to 28 guarantee individuals as well as groups the right to freedom of religion. However, Article 25 restricts the exercise of this right in the interests of public order, morality and health and all other rights enumerated in Part III of the Constitution. Therefore, it is constitutional for the legislature to place social welfare and reform over and above religious interests. In fact, Article 17 of the Constitution is a rare example of a penal constitutional provision which criminalizes untouchability ; a practice that can essentially be traced to Hinduism. Article 25, itself specifies that the freedom of religion cannot be used to restrict access to Hindu places of worship to upper castes. This relatively lower position that has been accorded to the freedom of religion in the Constitution is starkly different from the manner in which this has been played out in courts and political arenas in India. Many recent constitutional controversies in India have focused on religious rights. 1. How many articles in the Constitution guarantee 'Right to freedom of religion? a. 7 b. 6 c. 12 d. 9 2. Which article restricts the Right to freedom of religion under the rights enumerated in Part III of the Constitution? a. 29 b. 17 c. 25 d. 27 3. Which article criminalizes untouchability? a. 25 b. 17 c. 28 d. 29 4. What do the constitutional controversies recently focus on? a. Religious rights b. Religious tolerance c. Religious interests d. Religious practice 5. What is secularism? a. State supports religion b. State is separate from religion c. State Policy framework d. State supports public help help dkbaskdbnasdasda