The marketing department of a local shoe company found that approximately 550 pairs of running shoes are sold monthly when the price of each pair is $100. It was also observed that, for each $1 reduction in price, an additional 20 pairs of
running shoes are sold monthly. What price should the shoe store charge for a pair of running shoes in order to maximize revenue?

Answers

Answer 1

Answer:

The price that maximizes the revenue is $63.75

Step-by-step explanation:

Analyzing the statement one after the other.

[tex]Initial\ Quantity = 550[/tex]  ---- When ----- [tex]Initial\ Price = \$100[/tex]

When there's a reduction of $1, we have:

[tex]Quantity = 550 + 20x[/tex] and [tex]Price = 100 - x[/tex]

Where x represents the maximum reduction

At this point, we need to calculate the revenue (R)

[tex]R = Quantity * Price.[/tex]

[tex]R = (550 + 20x) * (100 - x)[/tex]

Open Brackets

[tex]R = 55000 - 550x + 2000x - 20x^2[/tex]

[tex]R = 55000 +1450x - 20x^2[/tex]

Differentiate both sides with respect to x

[tex]\frac{dR}{dx} = 0 + 1450 - 40x[/tex]

[tex]\frac{dR}{dx} = 1450 - 40x[/tex]

To maximize revenue;

[tex]\frac{dR}{dx} = 0[/tex]

So:

[tex]1450 - 40x = 0[/tex]

[tex]1450 =40x[/tex]

Solve for x

[tex]x = 1450/40[/tex]

[tex]x = 36.25[/tex]

Recall that:

[tex]Price = 100 - x[/tex]

Substitute [tex]x = 36.25[/tex]

[tex]Price = 100 - 36.25[/tex]

[tex]Price = 63.75[/tex]

Hence:

The price that maximizes the revenue is $63.75


Related Questions

Solve the formula for R:
PV = nRT

Answers

the answer is
r = pt/nT

Andrew paid for his burger with a 20% off coupon. If he paid $10 for his burger, what was the original price?

Answers

Answer:

20% off means that you subtract 20% of the price of the burger.

If the burger is $10, how much is 20% of that? If you subtract that amount, what do you get as the final price?

Step-by-step explanation:

the sum of a rational number and a irrational number

Answers

Answer: The sum of rational and irrational number is always irrational...

Answer:

When both rational and irrational numbers are written in decimal form, rational numbers can be written as finite decimals and infinite recurring decimals, such as 4=4.0, 4/5=0.8, 1/3=0.33333... and irrational numbers can only be written as infinite non-recurring decimals, such as √ 2=1.414213562…………According to this point, people define irrational numbers as infinite non-recurring decimals. 2. All rational numbers can be written as the ratio of two integers; irrational numbers cannot.

(Rational number): A number that can be accurately expressed as the ratio of two integers.    Such as 3, -98.11, 5.72727272..., 7/22 are all rational numbers.    Integers and fractions are all rational numbers. Rational numbers can also be divided into positive rational numbers, 0 and negative rational numbers.    Irrational numbers refer to infinite and non-recurring decimals such as: π   ·The difference between irrational and rational numbers:    1. When both rational and irrational numbers are written in decimal form, rational numbers can be written as finite decimals and infinite cyclic decimals.    For example, 4=4.0, 4/5=0.8, 1/3=0.33333... and irrational numbers can only be written as infinite and non-cyclic decimals.    For example, √2=1.414213562…………According to this point, people define irrational numbers as infinite and non-cyclic decimals.   2, all rational numbers can be written as the ratio of two integers; irrational numbers cannot. Based on this, some people suggested that irrational numbers should be removed from the "irrational" hat, and rational numbers should be called "comparative numbers" and irrational numbers should be called "irrational numbers". Originally, irrational numbers are not unreasonable, but people don't know much about it at first.   Using the main difference between rational and irrational numbers, we can prove that √2 is irrational.   Proof: Assume that √2 is not an irrational number, but a rational number.Since √2 is a rational number, it must be written as the ratio of two integers: √2 = p / q Since p and q do not have a common factor to be reduced, p / q can be considered to be the reduced fraction, the simplest form of fraction. Put √2 = p / q squared on both sides Get 2 = (p ^ 2)/(q ^ 2) Is 2 (q ^ 2) = p ^ 2 Since 2q ^ 2 is an even number, p must be an even number, so set p = 2m From 2 (q ^ 2) = 4 (m ^ 2) Get q ^ 2 = 2m ^ 2 Similarly, q must be an even number, let q = 2n Since p and q are both even numbers, they must have a common factor of 2, which contradicts the previous assumption that p/q is a reduced fraction. This contradiction is caused by the assumption that √2 is a rational number. Therefore √2 is an irrational number.

.

simplify this please


7^x ÷ 7^y

Answers

Answer:

[tex]\huge\boxed{7^{x-y}}[/tex]

Step-by-step explanation:

We can use basic exponent rules to simplify this expression.

We know that [tex]a^b \div a^c = a^{b-c}[/tex].

Since we have the same base (7) and different exponents (x, y), we can subtract the exponents and raise the base to that power.

[tex]7^{x-y}[/tex]

Hope this helped!

Which of the following represents the opposite of - 547
A plane descends 54 meters
The temperature is 54 degrees
Towe my friend $54
The miner traveled 54 meters below ground
C

Answers

$54 towe my friend degrees

Of the students in the marching band, 55%
plan to go to the school dance. If there are
110 students in the marching band that are
going to the dance, how many students
are in the marching band?

Answers

The answer is 200 because when you divide 110 from 55% you get 200.

Of the students in the marching band, 55% plan to go to the school dance, so there are 200 students in the marching band.

What is Percentage?

A certain portion or amount in every hundred is referred to as a percentage. The fraction is denoted by the sign "%," and its denominator is 100.

The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship between a component and a whole in which the value of the whole is always assumed to be 100.

From the given values in the question,

Assume that total number of students in marching band is x.

55% of x = 110 or,

(55/100) × x = 110

x = (110 × 100) / 55

x = 200.

Hence, it concludes that there are total 200 students are in the marching band.

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IF YOU CAN HELP ME I WILL LITERALLY BE SO HAPPY AND ILL FAV U TO GET SO MANY POINTS

THE WATER COMPANY INSTALLED A 40 YARD DIAGONAL BRACE ON A WATER TOWER BETWEEN TWO VERTICAL BEAMS THAT ARE 12 YARDS APART. DETERMINE THE HEIGHT OF EACH VERTICAL BEAM.

Answers

Answer:

120 yatds

Step-by-step explanation:

The height of each vertical beam is approximately 38.16 yards.

Would be great if I could get this answer, thank you:)

Answers

Answer:

160

Step-by-step explanation:

Find the area of the base

10 × 8 = 80

Multiply the height

80 × 6 = 480

then the the pyramid prism takes 1/3 so...

we then multiply 480 by 1/3

480 × 1/3 = 160

What is the y-intercept of y = 3 - 4x?

A: (0,3)
B: (3,0)
C: (-4,0)
D: (0,-4)

Answers

A is the right answer

Which of the four is it? ​

Answers

Answer:

option 1 i believe

Step-by-step explanation:

just worked it out

i hope this is right and helps <3

Create a code that will look at a single letter input. If the letter is a vowel, return the message "your letter is a vowel". Otherwise, return "your letter is a consonant."

Make sure that the code is in python. I will give brainliest to whoever answers the quickest. Thank you.

Answers

input=(“Enter a Letter ”)
if input = “a”, “e”, “i”, ”o”, ”u”
print(“You letter is a vowel”)

Please help I don't understand!!!!!!

Answers

Answer:

X-3

Step-by-step explanation:

The graph shifted 3 units to the left so you subtract from the x value.

3u(u-7k)-6k(k-8u) how?? ​

Answers

Explain the question more please

Frog and Toad decided to meet. Their houses are 120 ft apart. They start hopping towards each other at a speed of 2 ft/min and 3 ft/min, respectively. How long it will take until they are going to be 5 feet apart?

Answers

Answer:

23

Step-by-step explanation:

SOLVE AND JUSTIFY RIGHT ANSWER GETS BRAIN

Answers

Answer:

y is more than or equal to -1 5/23

Need help with this question plz help me

Answers

7/15-
There are 15 tiles in total. Three of them are yellow and four of them are green.

You add 3+4, and get 7. You put 7 over the total amount of tiles in the bag, which leads to 7/15.

Answer:

7/15

Step-by-step

The total amount of tiles is 15, then the total number of green and yellow tiles is 4 +3 = 7. Which means that the probability that you will get green or yellow tiles is the toltal amount of tiles of green and yellow tiles combined which is 7, compared to the total number of all tiles which is 15

7/15

Determine the intercepts of the line
X-intercept: (__ , __)
Y-intercept: (__, __)

Answers

Answer:

x-intercept (0.3,0)

y-intercept (0,0.4)

Step-by-step explanation:

The line crosses the Y axis at a height of o.4 and an x value of 0

the x axis is crossed at a distance of 0.3 and a height of 0

7,11,15,19 what is the zero term

Answers

Answer:

4n+3

Step-by-step explanation:

11-7=4, 15-11=4, 4(1) + something = 74(1)=4x1=44+something=7

So the nth term is 4n+3

Pls help 10th grade math

Answers

Answer:

B

Step-by-step explanation:

each side is corresponded to the other so Q=U and P=S

The correct option for the congruency of triangle by using ASA congruent theorem is,

⇒ ∠Q ≅ ∠T

We have to given that,

Two triangles PQR and STU are shown in figure.

Now, We have;

⇒ PQ ≅ ST

⇒ ∠P ≅ ∠S

To show the congruency of triangle by using ASA congruent theorem, we need;

⇒ ∠Q ≅ ∠T

As, PQ = ST

Therefore, The correct option for the congruency of triangle by using ASA congruent theorem is,

⇒ ∠Q ≅ ∠T

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write the equation to solve for x 3x + 21 6x - 60 please help i was given 3x+21=6x-60 thats wrong can someone please help richard u are amazing wish i could message u u can me​

Answers

Answer:

3x + 21 = 6x - 60

Step-by-step explanation:

parallel angles are equal

3x + 21 = 6x - 60

combine similar terms:

3x - 6x = -60 - 21

-3x = -81

x = 81/3

x = 27

now, plugin the value of x=27 back into the equation to get the angle:

= 3x + 21

= 3(27) + 21

= 102

= 6x - 60

= 6(27) - 60

= 102

as you noticed, both values are equal 102 = 102 because its a parallel angles

 

so the equation is 3x + 21 = 6x - 60

================================

i am pretty sure its correct.

You are filling piñatas for your sister's birthday party. The list shows the gifts you are putting into the piñatas. You want identical groups of gifts in each piñata with no gifts left over. What is the greatest number of piñatas you can make?

Answers

Answer:

The greatest number of piñatas you can make with the gifts is:

6 piñatas.

Step-by-step explanation:

To identify the greatest number of piñatas, you must think in a number that can divide another and obtain a whole number with this:

182442

Bigger the number, greater the number of piñatas, in this case, you can see the numbers given can be divided into four numbers obtaining a whole number: 1, 2, 3, and 6. Remember that the best number is the greatest, in this case, number six. Now you proceed to divide the numbers into 6:

[tex]\frac{18}{6}= 3[/tex][tex]\frac{24}{6}= 4[/tex] [tex]\frac{42}{6}=7[/tex]

Taking into account the values obtained, you can see that each piñata would have: 3 bottles of nail polish, 4 pairs of earrings, and 7 lollipops.

The ordered pairs below represent a relation. Is the relation a function? (4,6) (5,6) (6,7) (7,8)

Answers

Answer:

no because two inputs have the same outputs

Step-by-step explanation:

Which function is non linear y-4x=1 y=2+6x^4 x-2y=7

Answers

Answer:

12

Step-by-step explanation:

43

i will give brainliest solving x

Answers

Answer:

6

Step-by-step explanation:

What is 50000000000 + 500000000000

Answers

Answer:

1,000.000,000,000

Step-by-step explanation:

Answer:

free

Step-by-step explanation:

I was 6 my sister was half my age. I am 30 how old is she

Answers

Answer:

I think its 27.

Step-by-step explanation:

If they were 6 and her sister was half her age her sister would be 3. That means her sister is 3 years younger than they are. So if they are 30 all you do is 30 - 3 and you get your answer 27.

Hope this helps!

I need help plzz What is m 50*
35*
130*
95*

Answers

Answer:

50

Step-by-step explanation:

The measure of the angle ∠A will be 50°. The correct option is A.

What are lines and angles?

Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines. A figure called an angle is one in which two rays originate from the same point. In this area, you could also encounter contrasting and related viewpoints.

Given that the two angles are 85 and 145. The internal angles will be calculated as,

180 - 85 = 95

180 - 145 = 35

The angle A will be calculated as below,
∠A = 180 - 35 - 95

∠A = 50°

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Which pair of ratios is equivalent?
O A. 4:6 and 12:18
O B. 2:3 and 4:8
O C. 3:5 and 6:15
O D. 7:10 and 8:12

Answers

Answer:

A

Step-by-step explanation:

Both ratios simplify down to 2:3

Answer: 4:6 and 12:18

Step-by-step explanation:

Just took the test

CERTAIN ANSWERS ONLY!!! Please assist me, I will award you brain crown. thank you so much in advance :)

Answers

Answer:

See below.

Step-by-step explanation:

  Statements:                                         Reasons:

1) [tex]\overline{AB}\cong\overline{CD}; \overline{CE}\cong\overline{AE}[/tex]                           Given

2) [tex]AB=CD;CE=AE[/tex]                          Definition of Congruence

3) [tex]AE+EB=AB;CE+ED=CD[/tex]      Segment Addition Postulate

4) [tex]CE+EB=CD[/tex]                                   Substitution Property

5) [tex]CE+ED=CE+EB[/tex]                        Transitive Property

6) [tex]ED=EB[/tex]                                           Subtraction Property (of Equality)

7) [tex]\overline{ED}\cong\overline{EB}[/tex]                                          Definition of Congruence

Two pounds of ground beef will make 12 cups of chili. How many pounds of ground beef will Rashad need if he wants to make 18 cups of chili?

Answers

Answer:

Oh thats EZ

Step-by-step explanation:

He will need {3 POUNDS} to make 18 cups of chilli

Brainlist ??

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