Answer and Explanation:
The journal entries are shown below;
On Nov 1
Notes receivable-C.Bohr $62,400
To Cash $62,400
(Being cash paid is recorded)
On Dec 11
Notes receivable-K.R.Pine $1,800
To Sales revenue $1,800
(being sales revenue is recorded)
On Dec 16
Notes receivable-A.Murdock $9,600
To Account receivable $9,600
(Being note receivable is recorded)
On Dec 31
Interest receivable $767
To Interest revenue $767
(Being the interest revenue is recorded)
($62,400 × 7% × 2 ÷ 12 + $1,800 × 7% × 20 ÷ 360 + $9,600 × 8% × 15 ÷ 360)
A 30-year maturity bond with face value of $1,000 makes annual coupon payments and has a coupon rate of 8%. (Do not round intermediate calculations. Enter your answers as a percent rounded to 3 decimal places.)
Answer and Explanation:
a. The yield to maturity is
Given that
FV = $1000,
PV = -$900
PMT = 80 (8% of $1,000)
NPER = 30
The formula is
=RATE(NPER,PMT,-PV,FV,TYPE)
after applying the formula, the rate is 8.97%
b. In the case when the bond is sold at par so this means that yield to maturity is equivalent to the coupon rate i.e. 8%
c. The yield to maturity is
Given that
FV = $1000,
PV = -$1100
PMT = 80 (8% of $1,000)
NPER = 30
The formula is
=RATE(NPER,PMT,-PV,FV,TYPE)
after applying the formula, the rate is 7.18%
Given that annual deposit rates for Dollars and Euros are 8% and 6% respectively for the next 5 years. If the current spot rate of the Euro is $1.1845, obtain the implied rate for the Euro five years from now if International Fisher Equation (IFE) holds exactly.
a. $1.5415
b. $1.2742
c. $1.4284
d. $1.3750
e. None of the above.
Answer:
is the a
Explanation:
Assume that beer is an inferior good. If the price of beer falls, then the substitution effect results in the person buying ________ of the good and the income effect results in the person buying ________ of the good.
Answer:
more
less
Explanation:
Inferior goods are goods whose demand falls when income rises and increases when income falls.
When the price of beer changes, there are two effects that determine the quantity demanded. They are :
1. the substitution effect
2. the income effect
The substitution effect looks at the change in price of a good relative to other goods. When the price of beer decreases, it becomes cheaper relative to other goods. Thus, the demand for it increases.
The income effect looks at how a change in price affects real disposable income. When price of beer reduces, disposable income increases. Because beer is an inferior good, it would lead to a decrease in the demand for beer
Synovec Co. is growing quickly. Dividends are expected to grow at a rate of 22 percent for the next three years, with the growth rate falling off to a constant 5 percent thereafter. If the required return is 12 percent, and the company just paid a dividend of $2.35, what is the current share price
Answer:
53.98
Explanation:
current share price is the present value of dividends
Year 1 = 2.35 x 1.22 = 2.867
Year 2 = 2.867 x 1.22 = 3.50
Year 3 = 3.50 x 1.22 = 4.27
+ 4.27 x 1.05 / (0.12 - 0.05) = 64
I - 12%
PV = 53.98
To find the PV using a financial calculator:
1. Input the cash flow values by pressing the CF button. After inputting the value, press enter and the arrow facing a downward direction.
2. after inputting all the cash flows, press the NPV button, input the value for I, press enter and the arrow facing a downward direction.
3. Press compute
All sales are made on credit. Based on past experience, the company estimates 0.3% of net credit sales to be uncollectible. What adjusting entry should the company make at the end of the current year to record its estimated bad debts expense
Answer:
Missing word "A company uses the percent of sales method to determine its bad debts expense. At the end of the current year, the company's unadjusted trial balance reported the following selected amounts: Accounts receivable $350,000 debit, Allowance for uncollectible accounts 650 debit, Net Sales 795,000 credit"
Net credit sales = $795,000
Bad debt expense = 0.3% * Net credit sales
Bad debt expense = $795,000 * 0.3%
Bad debt expense = $2,385
Adjusting entry
Date General Journal Debit Credit
Bad debt expense $2,385
Allowance for uncollectible accounts $2,385
(To record bad debt expense)
A jewelry manufacturer incurred the following costs: 15,000 units produced with costs of $557,500, and 5,000 units produced with costs of $292,500. Which cost formula would you estimate using the high-low method? Group of answer choices Y=$265,000+$37.17X Y=$160,000+$17.67X Y=$265,000+$58.50X Y=$160,000+$26.50X
Answer:
Y=$160,000+$26.50X
Explanation:
Variable Cost = $26.50
Fixed Cost = $160,000
cost formula would you estimate using the high-low method : Y=$160,000+$26.50X
The demand curve for gasoline slopes downward and the supply curve for gasoline slopes upward. The production of the 200th gallon of gasoline entails the following:
• a private cost of $3.03;
• a social cost of $3.23;
• a value to consumers of $3.39.
Refer to Scenario 10-1. Suppose the equilibrium quantity of gasoline is 220 gallons; that is, Q MARKET = 220. Then the equilibrium price of a gallon could be:________
a. $3.08.
b.$2.77.
c. $2.45.
d. $3.69.
Answer:
a. $3.08
Explanation:
Calculation to determine what the equilibrium price of a gallon could be:
Based on the information given the Private cost is $3.03 while the Social cost is $3.23 which indicates that Social cost lies ABOVE the private cost and since The MARKET EQUILIBRIUM tend to occurs when Private value=Private cost which means that the EQUILIBRIUM PRICE lies between $3.03 and $3.23, Therefore the EQUILIBRIUM PRICE of a gallon would be $3.08 because it lies between $3.03 and $3.23.
The Abner Corporation, a retail seller of television sets, wants to determine how many television sets it must sell to earn a profit of $10,000 per month. The price of each television set is $300, and the average variable cost is $100. What is the required sales volume if the Abner Corporation’s monthly fixed costs are $5,000 per month?
Answer: 75
Explanation:
The required sales volume if the Abner Corporation’s monthly fixed costs are $5,000 per month will be:
Required sales = (Fixed cost + target profit) / (Selling price - AVC)
= (5,000 + 10,000) / (300 - 100)
= 15,000 / 200
= 75
Therefore, the required sales volume is 75.
________duties are tailored at the request of the Program Manager (PM) and are written in the Memorandum of Agreement, signed by both the PM and the Contract Administration Office (CAO) Commander (Please note the CAO Commander was previously referred to as the Contract Management Office (CMO) Commander).
a. Program Support Team
b. Administrative Contracting Officer
c. Program Integrator
d. Procuring Contracting Officer
Answer:
b. Administrative Contracting Officer
Explanation:
The officer who is given the responsibility of administering the U.S. government contracts in the Contract Administration Office is called the Administrative Contracting Officer (ACO). For the U.S. military, this office is led by the Contract Administration Office (CAO) Commander. The ACO in the CAO is just one of the officers under the CAO Commander, and she can negotiate contracts on behalf of the U.S. government.
SafeRide, Inc. produces air bag systems that it sells to North American automobile manufacturers. Although the company has a capacity of 300,000 units per year, it is currently producing at an annual rate of 180,000 units. SafeRide, Inc. has received an order from a German manufacturer to purchase 60,000 units at $9.00 each. Budgeted costs for 180,000 and 240,000 units are as follows: 180,000 Units 240,000 UnitsManufacturing costs Direct materials $450,000 $600,000Direct labor 315,000 420,000Factory overhead 1,215,000 1,260,000Total 1,980,000 2,280,000Selling and administrative 765,000 780,000Total $2,745,000 $3,060,000Costs per unit Manufacturing $11.00 $9.50Selling and administrative 4.25 3.25Total $15.25 $12.75Sales to North American manufacturers are priced at $20 per unit, but the sales manager believes the company should aggressively seek the German business even if it results in a loss of $3.75 per unit. She believes obtaining this order would open up several new markets for the company's product. The general manager commented that the company cannot tighten its belt to absorb the $225,000 loss ($3.75 × 60,000) it would incur if the order is accepted.(a) Determine the finanicial implications of accepting the order.(b) How would your analysis differ if the company were operating at capacity? Determine the advantage or disadvantage of accepting the order under full-capacity circumstances.
Answer:
SafeRide, Inc.
a. The financial implications of accepting the order are that total production cost will increase by $315,000 with a corresponding increase in sales revenue of $540,000, and an increase in net income by $225,000.
b. Under full capacity, the total production cost will increase by $1,485,000 for adding additional facilities while the sales revenue would increase by $540,000, resulting to a loss of $945,000.
c. Under full-capacity circumstances, there is a financing disadvantage of accepting the order because the order will entail additional capacity and facilities, resulting to a loss of $945,000.
Explanation:
Annual production capacity = 300,000 units
Current production capacity = 180,000 units
Special order from a German manufacturer = 60,000 units
Special order price per unit = $9.00
Budgeted Costs For 180,000 Units 240,000 Units Difference 60,000
Manufacturing costs
Direct materials $450,000 $600,000 $150,000
Direct labor 315,000 420,000 105,000
Factory overhead 1,215,000 1,260,000 45,000
Total 1,980,000 2,280,000 $300,000
Selling and administrative 765,000 780,000 15,000
Total $2,745,000 $3,060,000 $315,000
Costs per unit
Manufacturing $11.00 $9.50
Selling and administrative 4.25 3.25
Total $15.25 $12.75
Selling price to North American manufacturers = $20 per unit
Financial implications of accepting the order:
Manufacturing costs
Direct materials $150,000
Direct labor 105,000
Factory overhead 45,000
Total $300,000
Selling and administrative 15,000
Total $315,000
Total cost per unit = $5.25 ($315,000/60,000)
Total manufacturing cost per unit = $5 ($300,000/60,000)
Increase in net income from accepting the order = $225,000 ($9.00 - $5.25) * 60,000
Manufacturing costs
Direct materials $150,000 (variable)
Direct labor 105,000 (variable)
Factory overhead 1,215,000
Total $1,470,000
Selling and administrative 15,000 (assumed to be variable)
Total $1,485,000
Unit cost per additional unit = $24.75
At the beginning of May, Golden Gopher Company reports a balance in Supplies of $390. On May 15, Golden Gopher purchases an additional $2,200 of supplies for cash. By the end of May, only $190 of supplies remains. Required: 1.
Answer:
Missing word "rief Exercise 3-6 Parts 1 and 2 1. & 2. Record the necessary entries in the Journal Entry Worksheet below. (If no entry is required for a particular transaction/event, select "No journal entry required n the first account field.) view transaction list view general journal Journal Entry Worksheet Record the purchase of supplies. General Journal Debit Credit Date 2,600 May 15 Supplies expense Enter debits before credits clear entry record entry 7. 062 points Brief Exercise 3-6 Part 3 3. Calculate the balances after adjustment on May 31 of Supplies and Supplies Expense. Ending Balance Supplies Supplies expense"
1&2 Date General Journal Debit Credit
May 15 Supplies $2,200
Cash $2,200
May 31 Supplies expense $2,400
($390 + $2,200 - $190)
Supplies $2,400
3). Particulars Ending Balance
Supplies $190
Supplies expense $2,400
Gotham City acquires $25,000 of inventory on November 1, 20X7, having held no inventory previously. On December 31, 20X7, the end of Gotham City's fiscal year, a physical count shows $8,000 still in stock. During 20X8, $6,500 of this inventory is used, resulting in a $1,500 remaining balance of supplies on December 31, 20X8.
Based on the preceding information, what would be the correct account balances for 20X7 if Gotham City used the purchase method of accounting for inventories?
Answer:
$25,000; $8,000
Explanation:
Based on the information given , we were told that they acquires the amount of $25,000 of inventory on NOVEMBER 1, 20X7, in which on DECEMBER 31, 20X7, a PHYSICAL COUNT shows $8,000 was still in stock which means wthat the CORRECT ACCOUNT BALANCES for 20X7 if Gotham City used the PURCHASE METHOD of accounting for INVENTORIES will be Expenditure of the amount of $25,000 and Inventory of supplies of the amount of $8000.
The Adams Company is closely held and, therefore, cannot generate reliable inputs with which to use the CAPM method for estimating a company’s cost of internal equity. Adams’s bonds yield 10.28%, and the firm’s analysts estimate that the firm’s risk premium on its stock over its bonds is 4.95%. Based on the bond-yield-plus-risk-premium approach, Adams’s cost of internal equity is:
Answer:
the cost of internal equity is 16.17%
Explanation:
The computation of the cost of internal equity is shown below:
= Yield of the bond + risk premium of the firm
= 10.28% + 4.95%
= 16.17%
Hence, the cost of internal equity is 16.17%
Basically we add the two things so that the cost of internal equity could be determined
Agan Interiors provides home and office decorating assistance to customers. In normal operation 2.5 customers arrive per hour. One design consultant answers problems. The consultant averages 10 minutes per customer. Arrivals follow a Poisson distribution and the service times are exponentially distributed.
Required:
a. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times.
b. Service goals dictate that an arriving customer should not wait for service more than an average of 7 minutes. Is this goal being met? If not, what action do you recommend?
c. If the consultant can reduce the average time spent per customer to 9 minutes, what is the mean service rate?
Explanation:
we find the mean service rate at 10 minutes
= 60/10 = 6 min per hour
λ = 2.5
a.
1. we find the average number that are waiting in line
Lq = 2.5²/6(6-2.5)
= 6.25/21
= 0.2976
2. we find the average customers that are in this system
= 2.5²/6(6-2.5) + 2.5/6
= 0.2976 + 0.4167
L = 0.714266
approximately 0.7143
3. we have to determine the average time that a customers stays waitong
= Lq/λ
= 0.2976/2.5
= 0.11904 hours.
we convert this to minutes
= 0.11904 x 60
Wq = 7.1424 minutes
4. we find the average time that a customer is going to stay in the system
= 7.1424 + 60/6
w = 17.14 minutes
b. this goal is not being met here. This is because the service wait time is 7.14 minutes which is greater than 7 minutes. In order for them to meet this goal, they either have to hire other consultants or they have to raise their mean service rate.
c. mean would be =
60/9 = 6.67 per hour
Wq = 2.5/6.67(6.67-2.5)
= 2.5/27.814
= 0.0899 hour
= 0.0899*60
= 5.4 minutes
Other things equal, compared to using the first-in-first-out (FIFO) inventory cost method, using the last-in-first-out (LIFO) method in a rising price environment will result in a higher:____________
A. quick ratio.
B. inventory turnover ratio.
C. gross profit margin.
Answer:
B. inventory turnover ratio.
Explanation:
My best guess is that the inventory turnover ratio will be greater when LIFO is used during rising price environment because COGS will be higher and the inventory costs will be lower under LIFO than under FIFO.
Hope its correct.
This article seems to agree to some extent: https://smallbusiness.chron.com/impact-inflation-inventory-turnover-66227.html
Why is developing a reputation as a subject matter expert important for a leader if leadership deals so heavily with interpersonal skills
Answer:
Reputation is very important for a leader. If a leader has god interpersonal skills but lacks in good reputation people might hesitate to associate with him and support his activities.
Explanation:
Reputation is most valuable asset for any leader. A leader may have good knowledge of everything, he may have good interpersonal skills but reputation overcomes all of these qualities. Strong reputation of a leader will make it easy for him to earn popularity and respect among people. Reputation is the main quality which leads to success to a leader.
Navajo Corporation traded a used truck (cost $20,000, accumulated depreciation $18,000) for a small computer with a fair value of $3,300. Navajo also paid $500 in the transaction. Prepare the journal entry to record the exchange. (The exchange has commercial substance.)
Answer and Explanation:
The journal entry is given below:
Equipment/Computer $3,300
Accumulated depreciation-Truck $18,000
To Truck $20,000
To Gain on disposal of truck $800
To Cash $500
(Being the exchange is recorded)
Here the equipment and accumulated depreciation is debited as it increased the asset and credited the truck, cash and gain as it decreased the assets and increased the revenue
To what extent are moral ideas reflect society around us, and to what extent are we free to think for ourselves about moral matters?
Answer:
Moral ideas reflect society through collective behaviors that are presented by a large part of the population. These behaviors determine how far we are free to think about moral issues, as there is a social pressure that we associate our thoughts within this collective behavior.
Explanation:
Moral ideas determine what is right and wrong within society. This makes the population organize to act and behave in accordance with these oral ideas, collectively, always encouraging what is considered correct, good and progressive. This type of concept limits the freedom of individuals to think for themselves and reach their own conclusions about moral issues and social behavior, because there is pressure for the moral ideas accepted by most members of the population to be accepted without debate. For this reason, issues such as homosexuality, abortion, euthanasia, among others, are sources of criticism for a social minority, which decides to take a stand on these issues in a way contrary to the positing revealed as a moral idea by the majority of society.
Bantam company calculated its net income to be $38,775 based on the unadjusted trial balance. The following adjusting entries were then made for:
Salaries and wages owed but not yet paid of $395.
Interest earned but not received from investments of $375.
Prepaid insurance premiums amounting to $275 have expired.
Unearned revenue in the amount of $805 has now been earned.
Required:
Determine the amount of net income (loss) that will be reported after the adjustments are recorded.
Answer:
the amount of net income or loss is $39,285
Explanation:
The computation of the amount of net income or loss is shown below:
= Net income + interest earned + unearned revenue - salaries & wages - prepaid insurance
= $38,775 + $375 + $805 - $395 - $275
= $39,285
hence, the amount of net income or loss is $39,285
The same should be considered and relevant
Internal control procedures for cash receipts do not require that:_____.
a. Custody over cash is kept separate from its recordkeeping.
b. All collections for sales are received immediately upon making the sales.
c. Clerks having access to cash in a cash register should not have access to the register tape or file.
d. An employee with no access to cash receipts should compare the total cash recorded by the register with the record of cash receipts reported by the cashier.
e. Cash sales should be recorded on a cash register at the time of each sale.
f. All of these.
Answer:
b. All collections for sales are received immediately upon making the sales.
Explanation:
Internal control, regarded as a process used in assuring objective of an organization in operational effectiveness as well as efficiency and reliable financial reporting, it is also used in assuring of compliance with laws as well as regulations and policies. Generally, internal control can be described as everything which is able to controls risks to an organization. It is a way the
resources of an organization are been
measured as well as been directed and monitored.
It should be noted that Internal control procedures for cash receipts require that:.
✓Custody over cash is kept separate from its recordkeeping.
✓Clerks having access to cash in a cash register should not have access to the register tape or file.
✓An employee with no access to cash receipts should compare the total cash recorded by the register with the record of cash receipts reported by the cashier.
✓Cash sales should be recorded on a cash register at the time of each sale
C Corporation is investigating automating a process by purchasing a machine for $803,700 that would have a 9 year useful life and no salvage value. By automating the process, the company would save $138,500 per year in cash operating costs. The new machine would replace some old equipment that would be sold for scrap now, yielding $22,300. The annual depreciation on the new machine would be $89,300. The simple rate of return on the investment is closest to (Ignore income taxes.):
Answer:
6.30%
Explanation:
Calculation to determine what The simple rate of return on the investment is closest to
Using this formula
Simple rate of return= Annual net profit / net investment
Let plug in the formula
Simple rate of return= (138,500-89,300)/(803,700-22,300)
Simple rate of return= 49,200/781,400
Simple rate of return= 6.30%
Therefore The simple rate of return on the investment is closest to 6.30%
Each scenario below gives some information about price elasticity of demand for a firm. Use this information to answer the questions.
Honest Abe's Used Cars estimates the price elasticity of demand for their cars to be 5.10. Last month, Abe tried a new marketing scheme which decreased the number of cars sold by 57%.
Abe must have___prices. Abe's prices must have changed by___. Therefore, Abe's total revenue____.
At Webs-R-Us, a website design company, the new manager has decided to increase the price of Webs-R-Us services by 45%. If Webs-R-Us has a price elasticity of demand at 0.70, we can expected the number of websites designed to____. Therefore, Webs-R-Us's total revenue will The number of websites will change by_____.
Answer:
Increased
2.907%
decreased
decrease
increase
0.64
Explanation:
Price elasticity of demand measures the responsiveness of quantity demanded to changes in price of the good.
Price elasticity of demand = percentage change in quantity demanded / percentage change in price
Abe's elasticity of demand is elastic because it has a value greater than 1.
if quantity demanded decreases, it means that price must have been increased. this would lead to a decrease in total revenue
If the absolute value of price elasticity is greater than one, it means demand is elastic. Elastic demand means that quantity demanded is sensitive to price changes.
Demand is inelastic if a small change in price has little or no effect on quantity demanded. The absolute value of elasticity would be less than one
Demand is unit elastic if a small change in price has an equal and proportionate effect on quantity demanded.
Infinitely elastic demand is perfectly elastic demand. Demand falls to zero when price increases
Perfectly inelastic demand is demand where there is no change in the quantity demanded regardless of changes in price.
The following cost data relate to the manufacturing activities of Chang Company during the just completed year: Manufacturing overhead costs incurred: Indirect materials $ 17,000 Indirect labor 150,000 Property taxes, factory 10,000 Utilities, factory 90,000 Depreciation, factory 147,000 Insurance, factory 12,000 Total actual manufacturing overhead costs incurred $ 426,000 Other costs incurred: Purchases of raw materials (both direct and indirect) $ 420,000 Direct labor cost $ 80,000 Inventories: Raw materials, beginning $ 22,000 Raw materials, ending $ 32,000 Work in process, beginning $ 42,000 Work in process, ending $ 72,000 The company uses a predetermined overhead rate of $20 per machine-hour to apply overhead cost to jobs. A total of 21,700 machine-hours were used during the year. Required: 1. Compute the amount of underapplied or overapplied overhead cost for the year. 2. Prepare a schedule of cost of goods manufactured for the year.
Answer:
Part 1
under-applied overheads = $8,000
Part 2
Schedule of cost of goods manufactured for the year.
Opening Work in process $ 42,000
Add Direct Materials $393,000
Add Direct Labor $ 80,000
Add Applied Overheads $434,000
Less Ending Work In Process ( $ 72,000)
Cost of Goods Manufactured $877,000
Explanation:
The amount of underapplied or overapplied overhead cost for the year.
Applied Overheads = Predetermined overheads rate x Actual machine hours
= $20 x 21,700 machine-hours
= $434,000
Since,
actual manufacturing overhead costs = $ 426,000
and
applied manufacturing overhead = $434,000
then
under-applied overheads = $8,000 ($434,000 - $ 426,000)
Schedule of cost of goods manufactured for the year.
Opening Work in process $ 42,000
Add Direct Materials ($ 22 + $ 420 - $ 32 - $ 17) $393,000
Add Direct Labor $ 80,000
Add Applied Overheads $434,000
Less Ending Work In Process ( $ 72,000)
Cost of Goods Manufactured $877,000
Which of the following would be relevant in the make or buy decision? Direct materials Depreciation on equipment with no resale value A) Yes Yes B) Yes No C) No Yes D) No No
Answer:
B) Yes No
Explanation:
Materials cost are incremental and relevant whereas Depreciation on equipment with no resale value are irrelevant.
How many shares are held as treasury stock by Coca-Cola at December 31, 2015, and by PepsiCo at December 26, 2015
Answer:
December 31 ,2015 Coca cola and December 26, 2015
Fern invested $6400 into a continuously compounded account with an interest rate of 1.5%. After 10 years, how much is the account worth
Answer:
FV= $7,435.74
Explanation:
Giving the following information:
Initial investment= $6,400
Interest rate= 1.5%
Number of periods= 10 years
To calculate the value of the account in ten years, we need to use the following formula:
FV= PV*e^(i*n)
FV= 6,400*e^(0.015*10)
FV= $7,435.74
If a company has discriminated against minorities in the past, should it be required to give priority to minority applicants today? Why or why not?
Answer:
The description as per the given statement is summarized in the below segment.
Explanation:
There should priorities immigrants, although it has its inherent consequences since it damages the morality of all other project teams and thereby discourages them.This would also dissuade customer prejudice from purchasing the merchandise of the company and then so this might not be beneficial to priorities it. An invention that raises the future marginal product of capital in a closed economy) would cause an increase in desired investment, which would cause the investment curve to shift to the:________ and would cause the real interest rate to:________
A) right; increase
B) right; decrease
C) left: increase
D) left: decrease
Answer:
A) right; increase
Explanation:
In the case of the closed economy when the marginal product of capital increased so it also increased the investment due to which the shifting of the investment curve is rightward and this will result in increase in the real interest rate
So as per the given situation, the option a is correct
Calculate the geometric average return earned by an investor over three years if she earned 6% in the first year of an investment, 12% in the second year and 10% in the third year.
Answer:
8.96%
Explanation:
[tex]\sqrt[\frac{1}{n} ]{x1. x2.x3...}[/tex] = geometric average return
n = number of observations
x1 = observations
(0.06 x 0.12 x 0.1)^(1/3) = 0.0896 = 8.96%
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 per 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.)
$______
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
Determine the price that will yield a maximum profit
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
