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
Can someone please help me with this question?
Vanyuwa [196]

Answer:

5 seconds

Step-by-step explanation:

In 5 seconds it will be at 98 meters

x = -b/2a

x = -20/2(-2) = -20/-4 = 5

8 0
3 years ago
FIRST ANSWER IS BRAINLIEST IF CORRECT!!!A new clothing store had expenses of $60,000 for designing and building the shelves and
Mandarinka [93]
I Believe the answer is C. $ 120,000
4 0
3 years ago
6. If the net investment function is given by
Pachacha [2.7K]

The capital formation of the investment function over a given period is the

accumulated  capital for the period.

  • (a) The capital formation from the end of the second year to the end of the fifth year is approximately <u>298.87</u>.

  • (b) The number of years before the capital stock exceeds $100,000 is approximately <u>46.15 years</u>.

Reasons:

(a) The given investment function is presented as follows;

I(t) = 100 \cdot e^{0.1 \cdot t}

(a) The capital formation is given as follows;

\displaystyle Capital = \int\limits {100 \cdot e^{0.1 \cdot t}} \, dt =1000 \cdot  e^{0.1 \cdot t}} + C

From the end of the second year to the end of the fifth year, we have;

The end of the second year can be taken as the beginning of the third year.

Therefore,  for the three years; Year 3, year 4, and year 5, we have;

\displaystyle Capital = \int\limits^5_3 {100 \cdot e^{0.1 \cdot t}} \, dt \approx 298.87

The capital formation from the end of the second year to the end of the fifth year, C ≈ 298.87

(b) When the capital stock exceeds $100,000, we have;

\displaystyle  \mathbf{\left[1000 \cdot  e^{0.1 \cdot t}} + C \right]^t_0} = 100,000

Which gives;

\displaystyle 1000 \cdot  e^{0.1 \cdot t}} - 1000 = 100,000

\displaystyle \mathbf{1000 \cdot  e^{0.1 \cdot t}}} = 100,000 + 1000 = 101,000

\displaystyle e^{0.1 \cdot t}} = 101

\displaystyle t = \frac{ln(101)}{0.1} \approx 46.15

The number of years before the capital stock exceeds $100,000 ≈ <u>46.15 years</u>.

Learn more investment function here:

brainly.com/question/25300925

6 0
2 years ago
1) For question 1, use the figure below. a) Are the following polygons similar? Explain. (2 pts) Yes or No b) Assume the polygon
Delvig [45]

Answer: a) Yes b) Polygon ABCD ~ Polygon EFGH c) JKLM is 3x bigger than polygon ABCD

Step-by-step explanation:

(for part c)

JM= 36

AD= 12

36/12= 3

JKLM is 3x bigger than polygon ABCD

3 0
3 years ago
What is the solution to the inequality 1/2x(-2)&lt;8
kotegsom [21]
Ok I guess whatttt I do not getting it
6 0
3 years ago
Other questions:
  • 430 in scientific notation would be _____.
    6·1 answer
  • Bowls are purchased for $14 each and sold for $35.00. What is the percent of the markup based on cost?
    14·2 answers
  • Y varies directly as x and y = 18 when x= 1/2. write an equation that relates y and x
    8·1 answer
  • The original price is $75. She used a coupon code to receive a 20% discount. The web site applied a 10% service fee to the disco
    15·1 answer
  • A box contains 4 plain pencils and 4pens. A second box contains 3 color pencil and 5 crayons one item from each box is chosen at
    6·1 answer
  • What is the area of a<br> parallelogram with a base<br> of 2.5 cm and a height of<br> 6 cm?
    11·1 answer
  • Is 3/8 a natural whole integer or rational number
    10·2 answers
  • Janie bought a shirt at American Eagle and spent a total of $36.04, paying 6% in sales tax. The shirt was marked down 15% and wa
    5·2 answers
  • Gary has 5 3/5 acres of land. he uses 1/3 acres of the land for a shed a 1/6 of land for planting. how many acres of land does G
    11·1 answer
  • Need Help Asap ! i’ll mark brainly!!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!