Deck 4: Applications of the Derivative

Question 1

The owner of the Rancho Los Feliz has 2,600 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river.If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area?

A)
B)
C)
D)

Answer 1

Question 2

Phillip, the proprietor of a vineyard, estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $2/bottle.However, the profit from each bottle beyond 10,000 drops by $0.0004 for each additional bottle sold. Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? What would be the price/bottle in this case?

A)The maximum profit is $40,500.00, the price/bottle is $3.20/bottle
B)The maximum profit is $22,500.00, the price/bottle is $3.00/bottle
C)The maximum profit is $28,500.00,the price/bottle is $3.00/bottle
D)The maximum profit is $46,500.00, the price/bottle is $3.40/bottle
E)The maximum profit is $34,500.00, the price/bottle is $3.10/bottle

Answer 2

The maximum profit is $22,500.00, the price/bottle is $3.00/bottle

Question 3

An apple orchard has an average yield of 48 bushels of apples/tree if tree density is 26 trees/acre.For each unit increase in tree density, the yield decreases by 3 bushels.How many trees should be planted in order to maximize the yield?

A)23
B)24
C)22
D)21

Answer 3

21

Question 4

A Norman window has the shape of a rectangle surmounted by a semicircle (see the accompanying figure).If a Norman window is to have a perimeter of 28 ft, what should its dimensions be in order to allow the maximum amount of light through the window?

A)
B)
C)
D)

Question 5

A cylindrical container for storing radioactive waste is to be constructed from lead and have a thickness of 6 in.(see the figure).If the volume of the outside cylinder is to be , find the radius and the height of the inside cylinder that will result in a container of maximum storage capacity. Hint: Show that the storage capacity (inside volume) is given by

A)r = ft.; h = 2 ft.
B)r = ft.; h = 3 ft.
C)r = ft.; h = 2 ft.
D)r = ft.; h = 3 ft.

Question 6

A book designer has decided that the pages of a book should have margins at the top and bottom and margins on the sides.She further stipulated that each page should have an area of (see the figure). Determine the page dimensions that will result in the maximum printed area on the page.

A)
B)
C)
D)

Question 7

A grain silo has the shape of a right circular cylinder surmounted by a hemisphere (see the figure).If the silo is to have a capacity of , find the radius and height of the silo that requires the least amount of material to construct. Hint: The volume of the silo is , and the surface area (including the floor) is .

A)
B)
C)
D)

Question 8

The management of the UNICO department store has decided to enclose an 300 area outside the building for displaying potted plants and flowers.One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing material. If the pine board fencing costs $6/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost.

A)
B)
C)
D)

Question 9

A rectangular box is to have a square base and a volume of 32 .If the material for the base costs 10 cent/square foot, the material for the sides costs 30 cent/square foot, and the material for the top costs 20 cent/square foot, determine the dimensions of the box that can be constructed at minimum cost.

A)
B)
C)
D)

Question 10

For its beef stew, Betty Moore Company uses aluminum containers that have the form of right circular cylinders.Find the radius and height of a container if it has a capacity of and is constructed using the least amount of metal.

A)
B)
C)
D)

Question 11

In the diagram, S represents the position of a power relay station located on a straight coast, and E shows the location of a marine biology experimental station on an island.A cable is to be laid connecting the relay station with the experimental station. If the cost of running the cable on land is $2.50/running foot and the cost of running the cable under water is $6.50/running foot, locate the point P that will result in a minimum cost (solve for x).

A) ft
B) ft
C) ft
D) ft
E) ft

Question 12

A truck gets mpg when driven at a constant speed of x mph (between 40 and 80 mph).If the price of fuel is $1/gallon and the driver is paid $8/hour, at what speed between 40 and 80 mph is it most economical to drive?

A)60 mph
B)80 mph
C)40 mph
D)75 mph
E)45 mph

Question 13

The owner of a luxury motor yacht that sails among the 4,000 Greek islands charges $600/person/day if exactly 20 people sign up for the cruise.However,if more than 20 people sign up (up to the maximum capacity of 90) for the cruise, then each fare is reduced by $4 for each additional passenger. Assuming at least 20 people sign up for the cruise, determine how many passengers will result in the maximum revenue for the owner of the yacht.What is the maximum revenue? What would be the fare/passenger in this case?

A)85; $28,400; $340
B)90; $28,900; $350
C)90; $28,400; $350
D)85; $28,900; $340

Question 14

The demand for motorcycle tires imported by Dixie Import-Export is 40,000/year and may be assumed to be uniform throughout the year.The cost of ordering a shipment of tires is $400, and the cost of storing each tire for a year is $2. Determine how many tires should be in each shipment if the ordering and storage costs are to be minimized.(Assume that each shipment arrives just as the previous one has been sold.)

A)5,500
B)4,000
C)3,500
D)3,000

Question 15

What are the dimensions of a closed rectangular box that has a square cross section, a capacity of and is constructed using the least amount of material?

A)
B)
C)
D)
E)

Question 16

If exactly 150 people sign up for a charter flight, Leisure World Travel Agency charges $250/person.However, if more than 150 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Determine how many passengers will result in a maximum revenue for the travel agency.What is the maximum revenue? What would be the fare per passenger in this case?
Hint: Let x denote the number of passengers above 150.Show that the revenue function R is given by R(x) = (150 + x)(250 - x).

A)250; $39,000; $250
B)200; $40,000; $200
C)200; $39,000; $200
D)250; $40,000; $250

Question 17

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made.If the cardboard is 8 in.long and 3 in.wide, find the dimensions of the box that will yield the maximum volume.

A)
B)
C)
D)
E)

Question 18

Postal regulations specify that a parcel sent by parcel post may have a combined length and girth of no more than 102 in.Find the dimensions of a rectangular package that has a square cross section and the largest volume that may be sent through the mail.What is the volume of such a package? (Hint: The length plus the girth is (see the figure)).

A) ,
B) ,
C) ,
D) ,
E) ,

Question 19

If an open box has a square base and a volume of 500 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.

A)
B)
C)
D)

Question 20

A wooden beam has a rectangular cross section of height in.and width in.(see the figure).The strength of the beam is directly proportional to its width and the square of its height. What are the dimensions of the cross section of the strongest beam that can be cut from a round log of diameter 24 in.? Hint: , where is a constant of proportionality.

A)
B)
C)
D)

Question 21

What are the dimensions of a closed rectangular box that has a square cross section, a capacity of and is constructed using the least amount of material? Round the answer to two decimal places.

Question 22

An apple orchard has an average yield of 48 bushels of apples/tree if tree density is 24 trees/acre.For each unit increase in tree density, the yield decreases by 3 bushels.How many trees should be planted in order to maximize the yield?
__________ trees

Question 23

The demand for motorcycle tires imported by Dixie Import-Export is 30,000/year and may be assumed to be uniform throughout the year.The cost of ordering a shipment of tires is $300, and the cost of storing each tire for a year is $2.
Determine how many tires should be in each shipment if the ordering and storage costs are to be minimized.(Assume that each shipment arrives just as the previous one has been sold.)
__________ tires

Question 24

Neilsen Cookie Company sells its assorted butter cookies in containers that have a net content of 1 lb.The estimated demand for the cookies is 1,000,000 1-lb containers.The setup cost for each production run is $250, and the manufacturing cost is $.50 for each container of cookies.The cost of storing each container of cookies over the year is $.20.
Assuming uniformity of demand throughout the year and instantaneous production, how many containers of cookies should Neilsen produce per production run in order to minimize the production cost?
Hint: Show that the total production cost is given by the function .
Then minimize the function on the interval (0, 1,000,000).
__________ containers of cookies per production run

Question 25

A rectangular box is to have a square base and a volume of 4 .If the material for the base costs 20 cent/square foot, the material for the sides costs 30 cent/square foot, and the material for the top costs 10 cent/square foot, determine the dimensions of the box that can be constructed at minimum cost.

Question 26

Phillip, the proprietor of a vineyard, estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $2/bottle.However, the profit from each bottle beyond 10,000 drops by $0.0002 for each additional bottle sold.Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? Round the answer to two decimal places.
The maximum profit is $__________
What would be the price/bottle in this case? Round the answer to the nearest cent.
$__________/bottle

Question 27

Find the dimensions of a rectangle with a perimeter of 200 ft that has the largest possible area.

A)Dimensions are 100 ft.by 75 ft.
B)Dimensions are 65 ft.by 70 ft.
C)Dimensions are 65 ft.by 75 ft.
D)Dimensions are 60 ft.by 60 ft.
E)Dimensions are 50 ft.by 50 ft.

Question 28

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

A)Absolute maximum value: none; absolute minimum value:
B)Absolute maximum value: ; absolute minimum value: none
C)Absolute maximum value: ; absolute minimum value: none
D)No absolute extrema

Question 29

You are given the graph of some function f defined on the indicated interval.Find the absolute maximum and the absolute minimum of f, if they exist.

A)Absolute maximum value: 6; absolute minimum value: 0
B)Absolute maximum value: 4; absolute minimum value: - 1
C)Absolute maximum value: 3; absolute minimum value: - 1
D)Absolute maximum value: 6; absolute minimum value: - 1

Question 30

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made.If the cardboard is 8 in.long and 3 in.wide, find the dimensions of the box that will yield the maximum volume.

Question 31

If an open box has a square base and a volume of 864 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.

Question 32

You are given the graph of some function f defined on the indicated interval.Find the absolute maximum and the absolute minimum of f, if they exist.

A)Absolute maximum value: none; absolute minimum value: 0
B)Absolute maximum value: 7.4; absolute minimum value: none
C)Absolute maximum value: none; absolute minimum value: none
D)Absolute maximum value: 7.4; absolute minimum value: 0

Question 33

A book designer has decided that the pages of a book should have margins at the top and bottom and margins on the sides.She further stipulated that each page should have an area of (see the figure). Determine the page dimensions that will result in the maximum printed area on the page.

Question 34

Find the dimensions of a rectangle of area 144 sq ft that has the smallest possible perimeter.

A)Dimensions are 13 ft.by 11 ft.
B)Dimensions are 15ft.by 14 ft.
C)Dimensions are 12 ft.by 12 ft.
D)Dimensions are 10 ft.by 14 ft.
E)Dimensions are 9 ft.by 13 ft.

Question 35

The figure depicts a racetrack with ends that are semicircular in shape.The length of the track is . Find and so that the area enclosed by the rectangular region of the racetrack is as large as possible.

A)
B)
C)
D)

Question 36

The owner of the Rancho Los Feliz has 3,000 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river.
If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area?
__________

Question 37

Neilsen Cookie Company sells its assorted butter cookies in containers that have a net content of 1 lb.The estimated demand for the cookies is 1,000,000 1-lb containers.The setup cost for each production run is $250, and the manufacturing cost is $.30 for each container of cookies.The cost of storing each container of cookies over the year is $.20. Assuming uniformity of demand throughout the year and instantaneous production, how many containers of cookies should Neilsen produce per production run in order to minimize the production cost?
Hint: Show that the total production cost is given by the function .
Then minimize the function on the interval (0, 1,000,000).

A)50,000
B)40,000
C)45,000
D)35,000

Question 38

A truck gets mpg when driven at a constant speed of x mph (between 50 and 70 mph).If the price of fuel is $1/gallon and the driver is paid $8/hour, at what speed between 50 and 70 mph is it most economical to drive?
__________ mph

Question 39

Postal regulations specify that a parcel sent by parcel post may have a combined length and girth of no more than 84 in.
Find the dimensions of a rectangular package that has a square cross section and the largest volume that may be sent through the mail.Hint: The length plus the girth is (see the figure).
Dimensions: _____ x _____ x _____ What is the volume of such a package? __________

Question 40

In the diagram, S represents the position of a power relay station located on a straight coast, and E shows the location of a marine biology experimental station on an island.A cable is to be laid connecting the relay station with the experimental station. If the cost of running the cable on land is $3.60/running foot and the cost of running the cable under water is $6.00/running foot, locate the point P that will result in a minimum cost (solve for x). __________ ft

Question 41

Find the absolute maximum value and the absolute minimum value, if any, of the function.

A)Absolute maximum value: ; absolute minimum value:

B)Absolute maximum value: ; absolute minimum value:

C)Absolute maximum value: ; absolute minimum value:

D)Absolute maximum value: ; absolute minimum value:

E)Absolute maximum value: ; absolute minimum value:

Question 42

Suppose the quantity demanded per week of a certain dress is related to the unit price p by the demand equation , where p is in dollars and x is the number of dresses made. To maximize the revenue, how many dresses should be made and sold each week? (Hint: R(x) = px).Round the answer to the nearest integer.

A)333 dresses
B)330 dresses
C)335 dresses
D)338 dresses

Question 43

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

A)Absolute maximum value: ; absolute minimum value:

B)Absolute maximum value: ; absolute minimum value:

C)Absolute maximum value: none; absolute minimum value:
D)No absolute extrema

Question 44

Find the absolute maximum value and the absolute minimum value, if any, of the given function. on [1, 5]

A)Absolute maximum value: ; Absolute minimum value: 3
B)Absolute maximum value: ; Absolute minimum value:

C)Absolute maximum value: ; Absolute minimum value: 3
D)Absolute maximum value: ; Absolute minimum value: 4
E)Absolute maximum value: ; Absolute minimum value: 4

Question 45

Find the absolute maximum value and the absolute minimum value, if any, of the given function. on [1, 4]

A)Absolute maximum value: ; Absolute minimum value: 5
B)Absolute maximum value: ; Absolute minimum value: 4
C)Absolute maximum value: ; Absolute minimum value: 5
D)Absolute maximum value: ; Absolute minimum value: 4
E)Absolute maximum value: ; Absolute minimum value:

Question 46

A division of Chapman Corporation manufactures a pager.The weekly fixed cost for the division is $20,000, and the variable cost for producing x pagers/week is dollars. The company realizes a revenue of dollars from the sale of x pagers/week.
Find the level of production that will yield a maximum profit for the manufacturer.(Hint: Use the quadratic formula.)

A)1,316 pagers/week
B)1,666 pagers/week
C)1,616 pagers/week
D)1,542 pagers/week

Question 47

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

A)Absolute maximum value: ; absolute minimum value: none
B)Absolute maximum value: none; absolute minimum value: 0
C)Absolute maximum value: none; absolute minimum value:
D)No absolute extrema

Question 48

Find the absolute maximum value and the absolute minimum value, if any, of the function.

A)Absolute maximum value: 3; Absolute minimum value: 4
B)Absolute maximum value: 4; Absolute minimum value: none
C)Absolute maximum value: none; Absolute minimum value: 4
D)Absolute maximum value: 2; Absolute minimum value: 3
E)g(x) has no absolute extrema

Question 49

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

A)Absolute maximum value: ; absolute minimum value:

B)Absolute maximum value: ; absolute minimum value:

C)Absolute maximum value: ; absolute minimum value:

D)No absolute extrema

Question 50

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

A)Absolute maximum value: ; absolute minimum value:

B)Absolute maximum value: ; absolute minimum value:

C)Absolute maximum value: ; absolute minimum value:

D)No absolute extrema

Question 51

A stone is thrown straight up from the roof of a 50-ft building.The height (in feet) of the stone at any time t (in seconds), measured from the ground, is given by What is the maximum height the stone reaches?

A)99 ft
B)92 ft
C)110 ft
D)96 ft

Question 52

Find the absolute maximum value and the absolute minimum value, if any, of the function.

A)Absolute maximum value: 0; absolute minimum value: - 48
B)Absolute maximum value: 5; absolute minimum value: - 4
C)Absolute maximum value: 4; absolute minimum value: - 5
D)Absolute maximum value: 9; absolute minimum value: - 48
E)Absolute maximum value: 9; absolute minimum value: 0

Question 53

The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, manufactured by Phonola Record Industries, is related to the price/compact disc. The equation , where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price.
The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by .
To maximize its profits, how many copies should Phonola produce each month? Hint: The revenue is , and the profit is .

A)
B)
C)
D)
E)

Question 54

A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x rackets/day is given by Each racket can be sold at a price of p dollars, where p is related to x by the demand equation If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.

A)6,000 rackets/day
B)11,000 rackets/day
C)7,000 rackets/day
D)8,000 rackets/day

Question 55

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

A)Absolute maximum value: 199; absolute minimum value: - 1
B)Absolute maximum value: 3; absolute minimum value: - 1
C)Absolute maximum value: 3; absolute minimum value: - 109
D)Absolute maximum value: 199; absolute minimum value: - 109
E)No absolute extrema

Question 56

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

A)Absolute maximum value: 2; absolute minimum value: - 2
B)Absolute maximum value: 2; absolute minimum value: none
C)Absolute maximum value: 4; absolute minimum value: none
D)No absolute extrema

Question 57

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

A)Absolute maximum value: ; absolute minimum value:

B)Absolute maximum value: ; absolute minimum value:

C)Absolute maximum value: ; absolute minimum value:

D)No absolute extrema

Question 58

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

A)Absolute maximum value: ; absolute minimum value:

B)Absolute maximum value: ; absolute minimum value:

C)Absolute maximum value: ; absolute minimum value:

D)No absolute extrema

Question 59

The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of its model M1 camera is To maximize its profits, how many cameras should Cannon produce each month?

A)10,000 cameras
B)10,100 cameras
C)10,050 cameras
D)10,025 cameras

Question 60

Suppose the total cost function for manufacturing a certain product is dollars, where x represents the number of units produced.Find the level of production that will minimize the average cost.Round the answer to the nearest integer.

A)46 units
B)50 units
C)40 units
D)44 units

Question 61

The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of its model M1 camera is .
To maximize its profits, how many cameras should Cannon produce each month?
__________ cameras

Question 62

Find the horizontal and vertical asymptotes of the graph.

A)Horizontal asymptote is , vertical asymptote is

B)Horizontal asymptote is , vertical asymptote is

C)Horizontal asymptote is , vertical asymptote is

D)Horizontal asymptote is , vertical asymptote is

E)Horizontal asymptote is , vertical asymptote is

Question 63

A stone is thrown straight up from the roof of an 60-ft building.The height (in feet) of the stone at any time t (in seconds), measured from the ground, is given by .
What is the maximum height the stone reaches?
__________ ft

Question 64

Find the horizontal and vertical asymptotes of the graph.

A)Horizontal asymptotes: y = 3 and y = - 3
B)Vertical asymptotes: x = 3 and x = -3
C)Horizontal asymptotes: y = 3 and y = - 3; Vertical asymptote: x = 0
D)Horizontal asymptote: y = 1; Vertical asymptote: y = 3

Question 65

After the economy softened, the sky-high office space rents of the late 1990s started to come down to earth.The function R gives the approximate price per square foot in dollars, R(t), of prime space in Boston's Back Bay and Financial District from 1997 ( ) through 2000, where . What was the highest office space rent during the period in question? Hint: Use the quadratic formula.

A)$53.02 per sq ft
B)$52.92 per sq ft
C)$52.97 per sq ft
D)$53.07 per sq ft
E)$53.12 per sq ft

Question 66

Find the horizontal and vertical asymptotes of the graph.

A)Horizontal asymptote: y = 0.5
B)Horizontal asymptote: y = 0.5; Vertical asymptote: x = 0
C)Horizontal asymptotes: y = 0.5 and y = 1.5
D)Vertical asymptote: x = 0

Question 67

Suppose the quantity demanded per week of a certain dress is related to the unit price p by the demand equation , where p is in dollars and x is the number of dresses made.
To maximize the revenue, how many dresses should be made and sold each week? (Hint: R(x) = px.) Round the answer to the nearest integer.
__________ dresses

Question 68

If f is not continuous on the closed interval , then f cannot have an absolute maximum value.

A)false
B)true

Question 69

A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x rackets/day is given by Each racket can be sold at a price of p dollars, where p is related to x by the demand equation If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.
__________ rackets/day

Question 70

Answer true or false.
If f is defined on a closed interval , then f has an absolute maximum value.

Question 71

A division of Chapman Corporation manufactures a pager.The weekly fixed cost for the division is $20,000, and the variable cost for producing x pagers/week is dollars.The company realizes a revenue of dollars from the sale of x pagers/week.
Find the level of production that will yield a maximum profit for the manufacturer.(Hint: Use the quadratic formula.)
__________ pagers/week

Question 72

Lynbrook West, an apartment complex, has 100 two-bedroom units.The monthly profit (in dollars) realized from renting out x apartments is given by To maximize the monthly rental profit, how many units should be rented out? What is the maximum monthly profit realizable?

A)88 units are rented and the maximum monthly profit realizable is $23,720
B)22 units are rented and the maximum monthly profit realizable is $47,440
C)88 units are rented and the maximum monthly profit realizable ix $11,860
D)88 units are rented and the maximum monthly profit realizable is $47,440
E)44 units are rented and the maximum monthly profit realizable is $47,440

Question 73

The number of major crimes committed in the city of Bronxville between 1997 and 2004 is approximated by the function where N(t) denotes the number of crimes committed in year t ( corresponds to 1997).Enraged by the dramatic increase in the crime rate, the citizens of Bronxville with the help of the local police organized "Neighborhood Crime Watch" groups in early 2001 to combat this menace. When was the growth in the crime rate maximal?

A)2000
B)2001
C)2002
D)1999
E)2003

Question 74

The average speed of a vehicle on a stretch of a route between 6
A.M.At what time of the morning commute is the traffic moving at the slowest rate? What is the average speed of a vehicle at that time?
time = __________
A.M.average speed = __________ mph
A.M.and 10
A.M.on a typical weekday is approximated by the function
, where f (t) is measured in miles per hour and t is measured in hours, with t = 0 corresponding to 6

Question 75

The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation , where p is measured in dollars and x is measured in units of a thousand. To yield a maximum revenue, how many watches must be sold?

A)
B)
C)
D)
E)

Question 76

Find the horizontal and vertical asymptotes of the graph.

A)Horizontal asymptote: y = -2 ; vertical asymptote x = 0
B)Vertical asymptote: x = 0 .
C)Horizontal asymptotes: y = -2 and y = -3
D)Horizontal asymptote: y = -2

Question 77

The number of major crimes committed in the city between 1997 and 2004 is approximated by the function where N(t) denotes the number of crimes committed in year t ( corresponds to 1997).Enraged by the dramatic increase in the crime rate, the citizens, with the help of the local police, organized "Neighborhood Crime Watch" groups in early 2001 to combat this menace.
Show that the growth in the crime rate was maximal in 2003, giving credence to the claim that the Neighborhood Crime Watch program was working.

Question 78

The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, manufactured by Phonola Record Industries, is related to the price/compact disc.The equation , where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price.
The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by .
To maximize its profits, how many copies should Phonola produce each month? Hint: The revenue is , and the profit is . __________ copies

Question 79

The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation , where p is measured in dollars and x is measured in units of a thousand.
To yield a maximum revenue, how many watches must be sold? __________

Question 80

Suppose the total cost function for manufacturing a certain product is dollars, where x represents the number of units produced.Find the level of production that will minimize the average cost.Round the answer to the nearest integer.
__________ units