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
Grace [21]
1 year ago
8

the school newspaper has a circulation of 500 and sells for $.035 a copy. the students decide to raise the price to increase the

ir income and conduct a survey. they find for every $0.05 they increase the price they will lose 20 subscribers. what price per copy maximizes the income? solve and show work.
Mathematics
1 answer:
Alik [6]1 year ago
4 0

Let x be the number of times they raise the price on the newspaper. Then the new cost of the newspaper is

.35+.05x

Let y be the newspaper they sell, then the income will be

y(.35+.05x)

Now, we know that the circulation is of 500, assuming that they sold every newspaper at the original price now the number the will sell will be

y=500-20x

Plugging the value of y in the first expression we have that the income will be

\begin{gathered} f(x)=(500-20x)(.35+\text{0}.5x)=175+25x-7x-x^2 \\ =-x^2+18x+175 \end{gathered}

Then the income is given by the function

f(x)=-x^2+18x+175

To find the maximum value of this functions (thus the maximum income) we need to take the derivative of the function,

\begin{gathered} \frac{df}{dx}=\frac{d}{dx}(-x^2+18x+175) \\ =-2x+18 \end{gathered}

no we equate the derivative to zero and solve for x.

\begin{gathered} \frac{df}{dx}=0 \\ -2x+18=0 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}

This means that we have an extreme value of the function when x=9. Now we need to find out if this value is a maximum or a minimum. To do this we need to take the second derivative of the function, then

\begin{gathered} \frac{d^2f}{dx^2}=\frac{d}{dx}(\frac{df}{dx}) \\ =\frac{d}{dx}(-2x+18) \\ =-2 \end{gathered}

Since the second derivative is negative in the point x=9, we conclude that this value is a maximum of the function.

With this we conclude that the number of times that they should raise the price to maximize the income is 9. This means that they will raise the price of the newspaper (9)($0.05)=$0.45.

Therefore the price to maximize the income is $0.35+$0.45=$0.80.

You might be interested in
The sum of 3 times a number and 6 is 8.
Anastaziya [24]

Answer:

The number is 4/9

Step-by-step explanation:

3(6*(4/9))=3*(2+(2/3))=8

7 0
3 years ago
Read 2 more answers
Could someone please help me out? I've tried to solve this but I'm really having some trouble with it. Please try to explain it
guajiro [1.7K]

To find the area of the shaded region you need find the area of the shaded region and subtract the area of the unshaded region.

Area of a rectangle = width x length

A = (x + 10) x (2x + 5)

Next apply FOIL or First Outer Inner Last

A = (x * 2x) (x * 5) (10 * 2x) (10 * 5)

A= 2x2 + 5x + 20x + 50

A= 2x2 +25x +50

 

Area of a square=  sides2

A= (x + 1)2

A= (x+1) (x+1)

Next apply FOIL or First Outer Inner Last

A = (x *x) (1*x) (1*x) (1*1)

A = x2 + 1x + 1x +1

A= x2 + 2x +1

 

A= 2x2 +25x +50 - 2x2 +25x +50

A= 50x + 100





4 0
3 years ago
Please help!! what is the length of the line
UkoKoshka [18]

Answer:

\sqrt136 (option D)

<h3>Step-by-step explanation:</h3>

6 0
2 years ago
Urgent!!!! The scores of a high school entrance exam are approximately normally distributed with a given mean Mu = 82.4 and stan
Effectus [21]

Answer:95%

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Adrienne answered all 21 multiple choice questions correctly on her science test, if her teacher decides to let one of the quest
prisoha [69]
Since there are 21 questions and one is extra credit, the fraction is 21/20. Divide it to get 1.05. In percent, this is 105%. Hope this helps!
6 0
2 years ago
Other questions:
  • kia thinks she can make her new product for $5.80. She plans to sell for $12. what is her percent mark up?
    11·1 answer
  • please help :) What is 7.7 x 10 to the 8 power written in standard form? A. 770,000,000 B. 77,000,000,000 C. 77,000,000 D. 7,700
    8·1 answer
  • Trig help ..............
    11·1 answer
  • James started tutoring children several times a week. The first 2 weeks he had to buy tutoring supplies and had losses of $40 an
    6·1 answer
  • Write an addition equation that can help you 9-6 explain your answer
    12·1 answer
  • Find the difference between8÷15 and -−2÷3. Show all calculations in your final answer.
    10·1 answer
  • URGENT
    10·1 answer
  • Can someone plz help
    12·2 answers
  • Which property explains why these two expressions are equal? 7 + q + 4 = 4 + 7 + q
    9·1 answer
  • Joe ran 5/6 mile each day for 5 days. How far did joe run?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!