Question 1

The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system. The marketing department has determined that the demand for these speakers is  , where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded. Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be  .
Find the profit function P and select the graph of the profit function.

Accepted Answer

The answer of The management of Acrosonic plans to market...

Question 2

Williams Commuter Air Service realizes a monthly revenue of  dollars when the price charged per passenger is x dollars. Find the marginal revenue  .

Accepted Answer

The answer of Williams Commuter Air Service realizes a monthly...

Question 3

The total weekly cost (in dollars) incurred by a company in pressing x compact discs is  . What is the marginal cost when  and  ?

Accepted Answer

The answer of The total weekly cost (in dollars) incurred...

Question 4

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is  dollars/year. Find the average cost function C. Find the marginal average cost function  .

Accepted Answer

The answer of Custom Office makes a line of executive...

Question 5

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be  . The demand equation is  . Select the graph of the profit function.

Accepted Answer

The answer of Acrosonic's production department estimates that the total...

Question 6

The proprietor of the Showplace, a video store, has estimated that the rental price p (in dollars) of prerecorded video discs is related to the quantity x rented/day by the demand equation  Currently, the rental price is $2/disc. Is the demand elastic or inelastic at this rental price? If the rental price is increased, will the revenue increase or decrease?

Accepted Answer

The answer of The proprietor of the Showplace, a video...

Question 7

During the construction of an office building, a hammer is accidentally dropped from a height of 16 ft. The distance the hammer falls in t sec is  . What is the hammer's velocity when it strikes the ground? What is its acceleration?
The velocity is __________ ft per second.
The acceleration is __________ ft per second in the second power.

Accepted Answer

The answer of During the construction of an office building,...

Question 8

The weekly total cost function associated with manufacturing the Pulsar 25 color console television is given by  . What is the marginal average cost function  ?

Accepted Answer

The marginal average cost function is the derivative of the average cost function. We can find the average cost function by dividing the total cost function by the quantity, so:
AC = (TC/Q) = (11Q^3 + 2000) / Q = 11Q^2 + 2000/Q
Then, taking the derivative, we get:
MAC = d/dQ (AC) = 22Q - 2000/Q^2
So the answer is B, 11eaa8b1_dbe9_2973_b1b6_ade1ab118c95_TB6026_11.

Question 9

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is  dollars/year. Find the marginal average cost function  .

Accepted Answer

The answer of Custom Office makes a line of executive...

Question 10

The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor thermometer, has estimated that the total weekly cost (in dollars) for producing x thermometers is  dollars/year. Find the average cost function C.

Accepted Answer

The average cost function C is given by:

C(x) = Total cost / Quantity produced

C(x) = (11eaa8b1_dbe5_59c1_b1b6_c57009c92a8b_TB6026_11 dollars/year) / x

C(x) = 11eaa8b1_dbe5_80d3_b1b6_254efc73141b_TB6026_11

Therefore, the correct choice is B.

Question 11

The consumption function of the U.S. economy from 1929 to 1941 is  , where  is the personal consumption expenditure and  is the personal income, both measured in billions of dollars. Find the rate of change of consumption with respect to income,  . This quantity is called the marginal propensity to consume.

Accepted Answer

The answer of The consumption function of the U.S. economy...

Question 12

A division of Ditton Industries manufactures the Futura model microwave oven. The daily cost (in dollars) of producing these microwave ovens is where x stands for the number of units produced. What is the actual cost incurred in manufacturing the 301^st oven and the marginal cost when ?

Accepted Answer

The answer of A division of Ditton Industries manufactures the...

Question 13

The demand equation for the Roland portable hair dryer is given by  , where x (measured in units of a hundred) is the quantity demanded per week and p is the unit price in dollars. When is the demand unitary? (Hint: Solve  for p).

Accepted Answer

The answer of The demand equation for the Roland portable...

Question 14

The number of persons aged 18-64 receiving disability benefits through Social Security, the Supplemental Security income, or both, from 1990 through 2000 is approximated by the function  where  is measured in units of a million and t is measured in years, with t = 0 corresponding to the beginning of 1990.
Compute  . Round the answers to the nearest thousandth.  __________ million  __________ million per year  __________ million per year in the second power

Accepted Answer

The answer of The number of persons aged 18-64 receiving...

Question 15

Find the third derivative of the function.

Accepted Answer

The answer of Find the third derivative of the function....

Question 16

During testing of a certain brand of air purifier, the amount of smoke remaining t min after the start of the test was  percent of the original amount. Compute  . Round the answers to the nearest thousandth.  __________% per minute  __________% per minute in the second power

Accepted Answer

The answer of During testing of a certain brand of...

Question 17

Find the third derivative of the function.

Accepted Answer

The answer of Find the third derivative of the function....

Question 18

Pulsar manufactures a series of 19-in. color television sets. The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation  . The weekly total cost incurred by Pulsar for producing x sets is  dollars. Compute  ,  ,  .

Accepted Answer

The answer of Pulsar manufactures a series of 19-in. color...

Question 19

The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system. The marketing department has determined that the demand for these speakers is  , where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded. Find the marginal revenue function  .

Accepted Answer

The marginal revenue (MR) function is the derivative of the total revenue (TR) function.

Since the demand function is given as:
x = 110 - 2p

We can rewrite it as:
p = 55 - 0.5x

Therefore, the revenue function is:
TR = p*x
TR = (55 - 0.5x)*x
TR = 55x - 0.5x^2

Taking the derivative of TR with respect to x gives us the marginal revenue function:
MR = 55 - x

Substituting the demand function into this, we get:
MR = 55 - (110 - 2p)
MR = -55 + 2p

Simplifying this, we get:
MR = 2p - 55

Therefore, the correct answer is (B).

Question 20

The quantity of Sicard wristwatches demanded each month is related to the unit price by the equation  , where p is measured in dollars and x in units of a thousand. Find the marginal revenue function  .

Accepted Answer

The marginal revenue function is the derivative of the revenue function with respect to x.

R(x) = xp(x) = x(11 - 2x/1000)

Taking the derivative with respect to x, we get:

MR(x) = dR/dx = 11 - 4x/1000

Substituting the given equation for x, we get:

MR(p) = 11 - 4(1000ln(p/10))/1000

Simplifying:

MR(p) = 11 - 4ln(p/10)

Therefore, the correct choice is B.

Quiz 3: Differentiation

Williams Commuter Air Service realizes a monthly revenue of dollars when the price charged per passenger is x dollars. Find the marginal revenue .

The total weekly cost (in dollars) incurred by a company in pressing x compact discs is . What is the marginal cost when and ?

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is dollars/year. Find the average cost function C. Find the marginal average cost function .

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be . The demand equation is . Select the graph of the profit function.

The weekly total cost function associated with manufacturing the Pulsar 25 color console television is given by . What is the marginal average cost function ?

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is dollars/year. Find the marginal average cost function .

The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor thermometer, has estimated that the total weekly cost (in dollars) for producing x thermometers is dollars/year. Find the average cost function C.

A division of Ditton Industries manufactures the Futura model microwave oven. The daily cost (in dollars) of producing these microwave ovens is where x stands for the number of units produced. What is the actual cost incurred in manufacturing the 301^st oven and the marginal cost when ?

The demand equation for the Roland portable hair dryer is given by , where x (measured in units of a hundred) is the quantity demanded per week and p is the unit price in dollars. When is the demand unitary? (Hint: Solve for p) .

Find the third derivative of the function.

During testing of a certain brand of air purifier, the amount of smoke remaining t min after the start of the test was percent of the original amount. Compute . Round the answers to the nearest thousandth. % per minute % per minute in the second power

Find the third derivative of the function.

Pulsar manufactures a series of 19-in. color television sets. The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation . The weekly total cost incurred by Pulsar for producing x sets is dollars. Compute , , .

The quantity of Sicard wristwatches demanded each month is related to the unit price by the equation , where p is measured in dollars and x in units of a thousand. Find the marginal revenue function .

Quiz 3: Differentiation

Williams Commuter Air Service realizes a monthly revenue of dollars when the price charged per passenger is x dollars. Find the marginal revenue .

The total weekly cost (in dollars) incurred by a company in pressing x compact discs is . What is the marginal cost when and ?

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is dollars/year. Find the average cost function C. Find the marginal average cost function .

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be . The demand equation is . Select the graph of the profit function.

The weekly total cost function associated with manufacturing the Pulsar 25 color console television is given by . What is the marginal average cost function ?

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is dollars/year. Find the marginal average cost function .

The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor thermometer, has estimated that the total weekly cost (in dollars) for producing x thermometers is dollars/year. Find the average cost function C.

A division of Ditton Industries manufactures the Futura model microwave oven. The daily cost (in dollars) of producing these microwave ovens is where x stands for the number of units produced. What is the actual cost incurred in manufacturing the 301st oven and the marginal cost when ?

The demand equation for the Roland portable hair dryer is given by , where x (measured in units of a hundred) is the quantity demanded per week and p is the unit price in dollars. When is the demand unitary? (Hint: Solve for p) .

Find the third derivative of the function.

During testing of a certain brand of air purifier, the amount of smoke remaining t min after the start of the test was percent of the original amount. Compute . Round the answers to the nearest thousandth. __________% per minute __________% per minute in the second power

Find the third derivative of the function.

Pulsar manufactures a series of 19-in. color television sets. The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation . The weekly total cost incurred by Pulsar for producing x sets is dollars. Compute , , .

The quantity of Sicard wristwatches demanded each month is related to the unit price by the equation , where p is measured in dollars and x in units of a thousand. Find the marginal revenue function .

A division of Ditton Industries manufactures the Futura model microwave oven. The daily cost (in dollars) of producing these microwave ovens is where x stands for the number of units produced. What is the actual cost incurred in manufacturing the 301^st oven and the marginal cost when ?

During testing of a certain brand of air purifier, the amount of smoke remaining t min after the start of the test was percent of the original amount. Compute . Round the answers to the nearest thousandth. % per minute % per minute in the second power