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
atroni [7]
3 years ago
7

a gift shop sells 160 wind chimes per month at $150 each. the owners estimate that for each $15 increase in price, they will sel

l 5 fewer wind chimes per month. find the price per wind chime that will maximize revenue.
Mathematics
1 answer:
adell [148]3 years ago
3 0

Answer:

The price per wind chime that will maximize revenue = $ 315

Step-by-step explanation:

Given - A gift shop sells 160 wind chimes per month at $150 each. the owners estimate that for each $15 increase in price, they will sell 5 fewer wind chimes per month.

To find - Find the price per wind chime that will maximize revenue.

Proof -

Given that,

Total Wind chimes selling = 160

Price of each Wind chime = $150

Now,

Given that, for each $15 increase in price, they will sell 5 fewer wind chimes per month.

So,

Let the price = 150 + 15x

So,

Number of wind Chimes sold per month = 160 - 5x

So,

Total Revenue, R = (150 + 15x)(160 - 5x)

                             = 24000 - 750x + 2400x - 75x²

                             = 24000 + 1650x - 75x²

⇒R(x) = 24000 + 1650x - 75x²

Differentiate R with respect to x , we get

R'(x) = 1650 - 150x

Now,

For Maximize Revenue, Put R'(x) = 0

⇒1650 - 150x = 0

⇒150x = 1650

⇒x = 1650/150

⇒x = 11

∴ we get

Price per Wind chime = $ 150 + 15(11)

                                    = $ 150 + 165

                                    = $ 315

So,

The price per wind chime that will maximize revenue = $ 315

You might be interested in
What two steps are necessary to put this equation into standard form?
andrew-mc [135]
X² - 3x + 27 = 8x - 3     аdd 3 to both sides  ⇒
           + 3          + 3
---------------------------
x² - 3x + 30 = 8x         subtract 8x from both sides ⇒<span>
    - 8x          - 8x
--------------------------
x</span>² - 11x + 30 = 0    ←  <span>standard form
</span>

A. Add 3 to both sides and subtract 8x from both sides.
4 0
3 years ago
Read 2 more answers
URGENT! ANSWERS NEEDED​
a_sh-v [17]

7. 48000 Ounces

8. 1 pound and 4 ounces

9. 16 ounces = 1 pound

6 0
3 years ago
Read 2 more answers
What is the maximum area for a rectangle whose perimeter is 48 meters?
MakcuM [25]

Answer:

12m²

Step-by-step explanation:

For a rectangle, with length L and width W,

the perimeter is given as

Perimeter,

P = (2 x Length)  + (2 x Width)

P = 2L + 2W

It is given that the perimeter is 48, hence

48 = 2L + 2W   (divide both sides by 2)

24 = L + W

or

L = 24 - W -----> eq 1

Also realize that the Area of a Rectangle is given by

A = L x W  -----> eq 2

Substituting eq 1 into eq 2,

A = (24 - W) x W

A = -W² + 24W

Recall that for a quadratic equation y = ax² + bx + c, the maxima or minima is given by y(max) =  -b/2a

In this case, b = 24 and a = -1

-b/2a = -24/[ 2(-1) ] = 12

Hence for A to be maximum A(max) = 12m² (Answer)

5 0
3 years ago
Caleb and Sarah are having a valentines party. They hay 3 1/2 pounds of candy to divide 14 goodie bags.How much candy will be in
antoniya [11.8K]

Answer:

0.25 pounds of candy

Step-by-step explanation:

3.5 divided by 14 is 0.25

3 0
3 years ago
Caroline earns $54 babysitting for 6 hours
Lady_Fox [76]
It would be $9 per hour all you have to do is divide 54 by 6 you get 9, unit rate is 1

I hope this helps
6 0
3 years ago
Other questions:
  • Who wants free coins? just tell meh thx
    5·2 answers
  • Find the slope and y intercept for y=x+7
    14·1 answer
  • Jim received a $2000 loan from his bank. The loan accrues 3% interest every 3 months. How much will Jim owe the bank after 4 yea
    13·1 answer
  • What is 10/9 ? 9/8 closer to 0,1/2,1
    12·1 answer
  • Why are rates usually written as a unit rate
    13·1 answer
  • John is eating out with friends, and it is his turn to pay gratuity. The bill for the food is $48.53. If he plans to tip 20%, wh
    6·2 answers
  • Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two
    9·1 answer
  • Rectangle ABCD is transformed to A’B’C’D’ by a dilation. What is the scale factor used for the dilation?
    11·1 answer
  • A student wrote the equation 4(x+5.5)=3(1.5x+4.75) to represent the problem shown. Find her mistake and correct it.
    13·1 answer
  • =. What does the expression (x+3)(9) represent? Why?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!