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
iren2701 [21]
3 years ago
9

The quantity demanded x for a product is inversely proportional to the cube of the price p for p > 1. When the price is $10 p

er unit, the quantity demanded is 64 units. The initial cost is $140 and the cost per unit is $4. What price will yield a maximum profit? (Round your answer to two decimal places.)
$______
Business
1 answer:
Delvig [45]3 years ago
4 0

Answer:

$6.00

Explanation:

Given data

quantity demanded ( x )  ∝ 1 / p^3       for p > 1

when p = $10/unit , x = 64

initial cost = $140, cost per unit = $4

<u>Determine the price that will yield a maximum profit </u>

x = k/p^3 ----- ( 1 ).  when x = 64 , p = $10 , k = constant

64 = k/10^3

k = 64 * ( 10^3 )

  = 64000

back to equation 1

x = 64000 / p^3

∴ p = 40 / ∛x

next calculate the value of revenue generated

Revenue(Rx) = P(price ) * x ( quantity )

               = 40 / ∛x * x   =  40 x^2/3

next calculate Total cost of product

C(x) = 140 + 4x

Maximum Profit  generated = R(x) - C(x) = 0

                                              = 40x^2/3 - 140 + 4x  = 0

                                              =  40(2/3) x^(2/3 -1) - 0 - 4 = 0

                                            ∴ ∛x = 20/3    ∴     x = (20/3 ) ^3 = 296

profit is maximum at x(quantity demanded ) = 296 units

hence the price that will yield a maximum profit

P = 40 / ∛x

  = ( 40 / (20/3) )  = $6

                                             

You might be interested in
Ajay borrowed $6000 cash from his friend Tim, *
ad-work [718]

Answer:

Ajay account will be credited with $6000. While Tim account will be debited by $6000

6 0
3 years ago
Often, it is difficult to name a home country for a(n) ________ business
velikii [3]
Small business is difficult in the economy because its self made

8 0
3 years ago
Blossom Corp. will pay dividends of $5.00, $6.25, $4.75, and $3.00 in the next four years. Thereafter, management expects the di
Shkiper50 [21]

Answer:

Present value = $35.00326585 rounded off to $35.00

Explanation:

Using the dividend discount model, we calculate the price of the stock today. It values the stock based on the present value of the expected future dividends from the stock. To calculate the present value of the stock, we will use the following formula,

Present value = D1 / (1+r)  +  D2 / (1+r)^2  +  ...  +  Dn / (1+r)^n  +

[(Dn * (1+g)  /  (r - g))  /  (1+r)^n]

Where,

  • r is the required rate of return
  • g is the constant growth rate in dividends
  • n is the number of years

Present value = 5 / (1+0.155)  +  6.25 / (1+0.155)^2  + 4.75 / (1+0.155)^3  +  

3 / (1+0.155)^4  +  [(3 * (1+0.07)  /  (0.155 - 0.07))  /   (1+0.155)^4]

Present value = $35.00326585 rounded off to $35.00

3 0
3 years ago
Jackson company has the following financial information for their most recent fiscal year: Revenues Cost of Sales Interest Expen
irinina [24]

Answer:

The calculations are shown below

Explanation:

The computations are shown below:

But before that, first we have to prepare the income statement so that the values could come    

Particulars Amount  

Revenues $99,700  

Less: Cost of sales -$64,700  

Gross profit $35,000  

Less: Interest expenses -$1,800  

Earnings before tax $33,200  

Less: Taxes -$11,620  

Net income $21,580  

So, the calculations are shown below:

1. Earnings per share = Net income ÷ Common stock outstanding  

= $21,580 ÷ 16,000 shares    

= $1.35 per share

2. Price earnings ratio = Stock price per share ÷ Earnings per share  

= $22 ÷ $1.35    

= 16.3 times  

3. Long term debt to equity ratio  = Long term debt ÷ Total equity  

= $45,800 ÷ $120,000    

= 0.38 times  

4. Total market value = Number of shares outstanding × Market price per share

= 16,000 shares  × $22    

= $352,000  

4 0
3 years ago
Test the following sentences to see if headwords and verbs agree:
Maru [420]

Answer:

a). The statement on the income tax form about the deduction for children and other dependents was simply unreadable.

b). The type of career that many graduates are hoping to pursue pay high salaries and provide long vacations.

c). Apparently, the use of robots in factories has been responsible for a great deal of worker dissatisfaction.

d). The problems associated with government deregulation have been responsible for the economic plight of several major airlines in recent years.

e). The impact of computers on our lives is comparable to the impact of the industrial revolution.

f). The amount of money and time I spend on computer games <u>is</u> more than I can afford.

Explanation:

Subject-verb agreement is described as the grammatical rule according to which the subject, as well as, the verb must agree with one another in number. As per the rules, if the subject(noun or noun phrase) is singular, it will take a singular verb while if the subject is plural(noun or noun phrase), it will carry a plural verb.

According to this rule, <u>the first and third sentence fails to follow this agreement</u>. The first sentence inadequately carries a plural verb 'were' with the singular noun ('The statement') and similarly, the third sentence wrongly employs plural verb 'have' with the singular noun 'the use.' The other sentences are grammatically appropriate as the verbs and noun phrases agree in number.

3 0
3 years ago
Other questions:
  • The amount of money from a 529 college savings plan investment is dependent upon: A. college tuition inflation. B. the performan
    12·2 answers
  • One of the ways governments try to bring their (market) economies out of recession, to reduce unemployment, etc. is by
    15·2 answers
  • Under the TILA-RESPA Integrated Disclosure Rule (TRID), a lender must extend the closing how many days if the annual percentage
    15·1 answer
  • Culver Corporation has retained earnings of $718,500 at January 1, 2017. Net income during 2017 was $1,596,000, and cash dividen
    15·1 answer
  • A city ordered uniforms with an expected cost of $6,000 for policemen. This amount is encumbered.
    14·1 answer
  • Mary knits sweaters for sale. Her fixed costs are $100. When she makes 10 sweaters in one month, Mary must spend $15 on wool. To
    12·1 answer
  • Tanouye Corporation keeps careful track of the time required to fill orders. Data concerning a particular order appear below: Ho
    8·1 answer
  • Aulman Inc. has a number of divisions including a Furniture Division and a Motel Division. The Motel Division owns and operates
    15·1 answer
  • Undercapitalization refers to the problem of: Group of answer choices insufficient funds to operate a business normally. inadequ
    11·1 answer
  • In analyzing the pharmaceutical industry for a prospective business​ launch, nicole​ turco, a ph. D. In​ pharmacology, concluded
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!