Deck 8: Linear Programming Applications

Question 1

Linear programming variable names such as X₁₁,X₁₂,X₁₃,could possibly be used to represent production of a product (X_1j)over several months.

Answer 1

True

Question 2

A marketing research linear programming model can help a researcher structure the least expensive,statistically meaningful sample.

Answer 2

True

Question 3

Determining the mixture of ingredients for a most economical feed or diet combination would be described as a production mix type of linear program.

Answer 3

False

Question 4

Production scheduling is amenable to solution by LP because it is a problem that must be solved on a regular basis.

Question 5

The linear programming model of the production scheduling process is usually used when we have to schedule the production of multiple products,each of which requires a set of resources not required by the other products,over time.

Question 6

In formulating the media selection linear programming model,we are unable to take into account the effectiveness of a particular presentation (e.g. ,the fact that only 5 percent of the people exposed to a radio ad will respond as desired).

Question 7

The linear programming model of the production scheduling process is usually used when we have to schedule the production of a single product,requiring a mix of resources,over time.

Question 8

A media selection LP application describes a method in which media producers select customers.

Question 9

The linear programming model of the production mix problem only includes constraints of the less than or equal form.

Question 10

Blending problems arise when one must decide which of two or more ingredients is to be chosen to produce a product.

Question 11

Transporting goods from several origins to several destinations efficiently is called the transportation problem.

Question 12

The constraints in a transportation problem deal with requirements at each origin and capacities at each destination.

Question 13

Since the production mix linear program applications are a special situation,the number of decision variables is limited to two.

Question 14

An ingredient or blending problem is a special case of the more general problem known as diet and feed mix problems.

Question 15

In a production scheduling problem,the inventory at the end of this month is set equal to the inventory at the end of last month + last month's production − sales this month.

Question 16

The linear programming model of the production scheduling process can include the impact of hiring and layoffs,regular and overtime pay rates,and the desire to have a constant and stable production schedule over a several-month period.

Question 17

In general,linear programming is unable to solve complex labor planning as the objective function is usually not definable.

Question 18

The linear programming approach to media selection problems is typically to either maximize the number of ads placed per week or to minimize advertising costs.

Question 19

Another name for the transportation problem is the logistics problem.

Question 20

If a linear programming problem has alternate solutions,the order in which you enter the constraints may affect the particular solution found.

Question 21

In production scheduling LP problems,inventory at the end of this month is set equal to

A)inventory at the end of last month + this month's production - this month's sales.
B)inventory at the beginning of last month + this month's production - this month's sales.
C)inventory at the end of last month + last month's production - this month's sales.
D)inventory at the beginning of last month + last month's production - last month's sales.
E)inventory at the end of last month - this month's production + this month's sales.

Question 22

The linear programming transportation model allows us to solve problems where supply does not equal demand.

Question 23

Using linear programming to maximize audience exposure in an advertising campaign is an example of the type of linear programming application known as

A)media selection.
B)marketing research.
C)portfolio assessment.
D)media budgeting.
E)All of the above

Question 24

Table 8-1
A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 3 hours of assembly,2 hours of finishing,and 1 hour of inspection.Each chair requires 2 hours of assembly,2 hours of finishing,and 1 hour of inspection.The profit per table is $120 while the profit per chair is $80.Currently,each week there are 200 hours of assembly time available,180 hours of finishing time,and 40 hours of inspection time.Linear programming is to be used to develop a production schedule.Define the variables as follows:
T = number of tables produced each week
C = number of chairs produced each week
According to Table 8-1,which describes a production problem,which of the following would be a necessary constraint in the problem?

A)T + C ≤ 40
B)T + C ≤ 200
C)T + C ≤ 180
D)120T + 80C ≥ 1000
E)None of the above

Question 25

Table 8-1
A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 3 hours of assembly,2 hours of finishing,and 1 hour of inspection.Each chair requires 2 hours of assembly,2 hours of finishing,and 1 hour of inspection.The profit per table is $120 while the profit per chair is $80.Currently,each week there are 200 hours of assembly time available,180 hours of finishing time,and 40 hours of inspection time.Linear programming is to be used to develop a production schedule.Define the variables as follows:
T = number of tables produced each week
C = number of chairs produced each week
According to Table 8-1,which describes a production problem,what would the objective function be?

A)Maximize T + C
B)Maximize 120T + 80C
C)Maximize 200T + 200 C
D)Minimize 6T + 5C
E)None of the above

Question 26

Table 8-2
Diamond Jeweler's is trying to determine how to advertise in order to maximize their exposure.Their weekly advertising budget is $10,000.They are considering three possible media: tv,newspaper,and radio.Information regarding cost and exposure is given in the table below: Let T = the # of tv ads,N = the # of newspaper ads,and R = the # of radio ads
According to Table 8-2,which describes a media selection problem,what would the objective function be?

A)Maximize 10T + 7N + 20R
B)Minimize 10T + 7N + 20R
C)Minimize 800T + 1000N + 400R
D)Minimize 7000T + 8500N + 3000R
E)Maximize 7000T + 8500N + 3000R

Question 27

Table 8-1
A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 3 hours of assembly,2 hours of finishing,and 1 hour of inspection.Each chair requires 2 hours of assembly,2 hours of finishing,and 1 hour of inspection.The profit per table is $120 while the profit per chair is $80.Currently,each week there are 200 hours of assembly time available,180 hours of finishing time,and 40 hours of inspection time.Linear programming is to be used to develop a production schedule.Define the variables as follows:
T = number of tables produced each week
C = number of chairs produced each week
According to Table 8-1,which describes a production problem,suppose it is decided that the number of hours used in the assembly process must be at least 80 percent of the time available.How would this constraint be written?

A)3T + 2C ≥ 160
B)3T + 2C ≥ 200
C)3T + 2C ≤ 200
D)3T + 2C ≤ 160
E)None of the above

Question 28

Table 8-1
A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 3 hours of assembly,2 hours of finishing,and 1 hour of inspection.Each chair requires 2 hours of assembly,2 hours of finishing,and 1 hour of inspection.The profit per table is $120 while the profit per chair is $80.Currently,each week there are 200 hours of assembly time available,180 hours of finishing time,and 40 hours of inspection time.Linear programming is to be used to develop a production schedule.Define the variables as follows:
T = number of tables produced each week
C = number of chairs produced each week
According to Table 8-1,which describes a production problem,suppose it is decided that the number of hours used in the assembly process must be at least 90 percent of the number of hours used in the finishing department.How would this constraint be written?

A)3T + 2C ≥ 162
B)3T + 2C ≥ 0.9(2T + 2C)
C)3T + 2C ≤ 162
D)3T + 2C ≤ 0.9(2T + 2C)
E)None of the above

Question 29

Table 8-1
A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 3 hours of assembly,2 hours of finishing,and 1 hour of inspection.Each chair requires 2 hours of assembly,2 hours of finishing,and 1 hour of inspection.The profit per table is $120 while the profit per chair is $80.Currently,each week there are 200 hours of assembly time available,180 hours of finishing time,and 40 hours of inspection time.Linear programming is to be used to develop a production schedule.Define the variables as follows:
T = number of tables produced each week
C = number of chairs produced each week
According to Table 8-1,which describes a production problem,which of the following would be a necessary constraint in the problem?

A)T + C ≥ 40
B)3T + 2C ≤ 200
C)2T + 2C ≤ 40
D)120T + 80C ≥ 1000
E)None of the above

Question 30

Media selection problems are typically approached with LP by either

A)maximizing audience exposure or maximizing number of ads per time period.
B)maximizing the number of different media or minimizing advertising costs.
C)minimizing the number of different media or minimizing advertising costs.
D)maximizing audience exposure or minimizing advertising costs.
E)minimizing audience exposure or minimizing advertising costs.

Question 31

Which of the following does not represent a factor a manager might typically consider when employing linear programming for a production scheduling?

A)labor capacity
B)space limitations
C)product demand
D)risk assessment
E)inventory costs

Question 32

Which of the following is considered a decision variable in the media selection problem of minimizing interview costs in surveying?

A)the number of people to survey in each market segment
B)the overall survey budget
C)the total number surveyed
D)the number of people to conduct interviews
E)None of the above

Question 33

The linear programming ingredient or blending problem model allows one to include not only the cost of the resource,but also the differences in composition.

Question 34

The selection of specific media from among a wide variety of alternatives is the type of LP problem known as

A)the product mix problem.
B)the investment banker problem.
C)the Wall Street problem.
D)the portfolio selection problem.
E)None of the above

Question 35

Table 8-2
Diamond Jeweler's is trying to determine how to advertise in order to maximize their exposure.Their weekly advertising budget is $10,000.They are considering three possible media: tv,newspaper,and radio.Information regarding cost and exposure is given in the table below: Let T = the # of tv ads,N = the # of newspaper ads,and R = the # of radio ads
According to Table 8-2,what is the advertising budget constraint?

A)10T + 7N + 20R ≤ 10,000
B)10T + 7N + 20R ≥ 10,000
C)800T + 1000N + 400R ≤ 10,000
D)800T + 1000N + 400R ≥ 10,000
E)7000T + 8500N + 3000R ≤ 10,000

Question 36

In the linear programming transportation model,the coefficients of the objective function can represent either the cost or the profit from shipping goods along a particular route.

Question 37

The linear programming truck loading model always results in a practical solution.

Question 38

Which of the following is considered a decision variable in the production mix problem of maximizing profit?

A)the amount of raw material to purchase for production
B)the number of product types to offer
C)the selling price of each product
D)the amount of each product to produce
E)None of the above

Question 39

Table 8-1
A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 3 hours of assembly,2 hours of finishing,and 1 hour of inspection.Each chair requires 2 hours of assembly,2 hours of finishing,and 1 hour of inspection.The profit per table is $120 while the profit per chair is $80.Currently,each week there are 200 hours of assembly time available,180 hours of finishing time,and 40 hours of inspection time.Linear programming is to be used to develop a production schedule.Define the variables as follows:
T = number of tables produced each week
C = number of chairs produced each week
According to Table 8-1,which describes a production problem,suppose it is decided that there must be 4 chairs produced for every table.How would this constraint be written?

A)T ≥ C
B)T ≤ C
C)4T = C
D)T = 4C

Question 40

Which of the following is considered a decision variable in the media selection problem of maximizing audience exposure?

A)the amount spent on each ad type
B)what types of ads to offer
C)the number of ads of each type
D)the overall advertising budget
E)None of the above

Question 41

Table 8-6
The following is a linear programming formulation of a labor planning problem.There are four overlapping shifts,and management must decide how many employees to schedule to start work on each shift.The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day.The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
According to Table 8-6,which describes a labor planning problem and its solution,how many workers would be assigned to shift 4?

A)1
B)0
C)14
D)16
E)None of the above

Question 42

Table 8-5
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9.Each bookcase yields a $12 profit.Kent's firm is small and its resources limited.During any given production period (of 1 week),10 gallons of varnish and 12 lengths of high quality redwood are available.Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood.Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
T = number of tables produced each week
B = number of bookcases produced each week
Referring to Table 8-5,which of the following constraints would be used?

A)maximize 9T + 12B
B)9T + 12B ≥ 12
C)12T + 9B ≤ 10
D)10T + 10B ≥ 10
E)None of the above

Question 43

Table 8-5
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9.Each bookcase yields a $12 profit.Kent's firm is small and its resources limited.During any given production period (of 1 week),10 gallons of varnish and 12 lengths of high quality redwood are available.Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood.Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
T = number of tables produced each week
B = number of bookcases produced each week
Referring to Table 8-5,suppose that this problem requires that you use all the varnish for the week.How would the linear programming representation change?

A)1B + 1T ≤ 10 will become 1B + 1T ≤ 12.
B)1B + 1T ≤ 10 will be replaced by 1B + 1T ≥ 10.
C)1B + 1T ≤ 10 will become 1B + 1T = 10.
D)2B + 1T ≤ 12 will become 2B + 1T = 12.
E)None of the above

Question 44

Table 8-4
A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 4 hours of assembly,3 hours of finishing,and 1 hour of inspection.Each chair requires 3 hours of assembly,2 hours of finishing,and 2 hours of inspection.The selling price per table is $140 while the selling price per chair is $90.Currently,each week there are 220 hours of assembly time available,160 hours of finishing time,and 45 hours of inspection time.Assume that one hour of assembly time costs $5.00;one hour of finishing time costs $6.00;one hour of inspection time costs $4.50;and that whatever labor hours are not required for the table and chairs can be applied to another product.Linear programming is to be used to develop a production schedule.Define the variables as follows:
T = number of tables produced each week
C = number of chairs produced each week
Suppose that the problem described in Table 8-4 is modified to specify that one-third of the tables produced must have 6 chairs,one-third must have 4 chairs,and one-third must have 2 chairs.How would this constraint be written?

A)C = 4T
B)C = 2T
C)C = 3T
D)C = 6T
E)None of the above

Question 45

Table 8-5
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9.Each bookcase yields a $12 profit.Kent's firm is small and its resources limited.During any given production period (of 1 week),10 gallons of varnish and 12 lengths of high quality redwood are available.Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood.Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
T = number of tables produced each week
B = number of bookcases produced each week
Referring to Table 8-5,the solution to the problem is

A)T = 10,B = 0.
B)T = 0,B = 10.
C)T = 0,B = 6.
D)T = 8,B = 2.
E)None of the above

Question 46

Table 8-6
The following is a linear programming formulation of a labor planning problem.There are four overlapping shifts,and management must decide how many employees to schedule to start work on each shift.The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day.The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
According to Table 8-6,which describes a labor planning problem and its solution,how many workers would be assigned to shift 2?

A)2
B)0
C)14
D)15
E)None of the above

Question 47

Table 8-6
The following is a linear programming formulation of a labor planning problem.There are four overlapping shifts,and management must decide how many employees to schedule to start work on each shift.The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day.The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
According to Table 8-6,which describes a labor planning problem and its solution,how many workers would be assigned to shift 1?

A)12
B)13
C)0
D)2
E)None of the above

Question 48

Table 8-3
A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education.There are different cost implications for the region of the country where the college is located and the type of degree.The survey cost table is provided below: The requirements for the survey are as follows:
1.The survey must have at least 1500 students
2.At least 400 graduate students
3.At least 100 graduate students should be from the West
4.No more than 500 undergraduate students should be from the East
5.At least 75 graduate students should be from the Central region
6.At least 300 students should be from the West
The marketing research firm would like to minimize the cost of the survey while meeting the requirements.Let X₁ = # of undergraduate students from the East region,X₂ = # of graduate students from the East region,X₃ = # of undergraduate students from the Central region,X₄ = # of graduate students from the Central region,X₅ = # of undergraduate students from the West region,and X₆ = # of graduate students from the West region.
According to Table 8-3,what is the objective function?

A)Minimize 10X₁ + 15X₂ + 12X₃ + 18X₄ + 15X₅ + 21X₆
B)Maximize 10X₁ + 15X₂ + 12X₃ + 18X₄ + 15X₅ + 21X₆
C)Minimize 10X₁ + 12X₂ + 15X₃ + 15X₄ + 18X₅ + 21X₆
D)Maximize 10X₁ + 12X₂ + 15X₃ + 15X₄ + 18X₅ + 21X₆
E)Minimize 1500X₁ + 400X₂ + 100X₃ + 500X₄ + 75X₅ + 300X₆

Question 49

Table 8-2
Diamond Jeweler's is trying to determine how to advertise in order to maximize their exposure.Their weekly advertising budget is $10,000.They are considering three possible media: tv,newspaper,and radio.Information regarding cost and exposure is given in the table below: Let T = the # of tv ads,N = the # of newspaper ads,and R = the # of radio ads
According to Table 8-2,which of the following set of inequalities properly represent the limits on advertisements per week by media?

A)T ≤ 10;N ≤ 7;R ≤ 20
B)T ≥ 10;N ≥ 7;R ≥ 20
C)T + R + N ≤ 37
D)T + R + N ≥ 37
E)10N + 7N + 20T ≤ 10,000

Question 50

Table 8-6
The following is a linear programming formulation of a labor planning problem.There are four overlapping shifts,and management must decide how many employees to schedule to start work on each shift.The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day.The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
According to Table 8-6,which describes a labor planning problem and its solution,how many workers would actually be on duty during shift 1?

A)12
B)13
C)0
D)29
E)None of the above

Question 51

Table 8-4
A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 4 hours of assembly,3 hours of finishing,and 1 hour of inspection.Each chair requires 3 hours of assembly,2 hours of finishing,and 2 hours of inspection.The selling price per table is $140 while the selling price per chair is $90.Currently,each week there are 220 hours of assembly time available,160 hours of finishing time,and 45 hours of inspection time.Assume that one hour of assembly time costs $5.00;one hour of finishing time costs $6.00;one hour of inspection time costs $4.50;and that whatever labor hours are not required for the table and chairs can be applied to another product.Linear programming is to be used to develop a production schedule.Define the variables as follows:
T = number of tables produced each week
C = number of chairs produced each week
According to Table 8-4,which describes a production problem,suppose you realize that you can trade off assembly hours for finishing hours,but that the total number of finishing hours,including the trade-off hours,cannot exceed 240 hours.How would this constraint be written?

A)7T + 5C ≤ 360
B)3T + 2C ≤ 240
C)4T + 3C ≤ 140
D)−T − C ≤ 80
E)None of the above

Question 52

Table 8-3
A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education.There are different cost implications for the region of the country where the college is located and the type of degree.The survey cost table is provided below: The requirements for the survey are as follows:
1.The survey must have at least 1500 students
2.At least 400 graduate students
3.At least 100 graduate students should be from the West
4.No more than 500 undergraduate students should be from the East
5.At least 75 graduate students should be from the Central region
6.At least 300 students should be from the West
The marketing research firm would like to minimize the cost of the survey while meeting the requirements.Let X₁ = # of undergraduate students from the East region,X₂ = # of graduate students from the East region,X₃ = # of undergraduate students from the Central region,X₄ = # of graduate students from the Central region,X₅ = # of undergraduate students from the West region,and X₆ = # of graduate students from the West region.
According to Table 8-3,the minimum cost is

A)20500
B)20000
C)18950
D)19625
E)19400

Question 53

Table 8-2
Diamond Jeweler's is trying to determine how to advertise in order to maximize their exposure.Their weekly advertising budget is $10,000.They are considering three possible media: tv,newspaper,and radio.Information regarding cost and exposure is given in the table below: Let T = the # of tv ads,N = the # of newspaper ads,and R = the # of radio ads
According to Table 8-2,what is the optimal solution?

A)T = 10;N = 7;R = 20
B)T = 10;N = 0;R = 0
C)T = 10;N = 2;R = 0
D)Solution is unbounded
E)Solution is infeasible

Question 54

Table 8-3
A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education.There are different cost implications for the region of the country where the college is located and the type of degree.The survey cost table is provided below: The requirements for the survey are as follows:
1.The survey must have at least 1500 students
2.At least 400 graduate students
3.At least 100 graduate students should be from the West
4.No more than 500 undergraduate students should be from the East
5.At least 75 graduate students should be from the Central region
6.At least 300 students should be from the West
The marketing research firm would like to minimize the cost of the survey while meeting the requirements.Let X₁ = # of undergraduate students from the East region,X₂ = # of graduate students from the East region,X₃ = # of undergraduate students from the Central region,X₄ = # of graduate students from the Central region,X₅ = # of undergraduate students from the West region,and X₆ = # of graduate students from the West region.
According to Table 8-3,the constraint that the survey must have at least a total of 1500 students is expressed as

A)X₁ + X₂ + X₃ + X₄ + X₅ + X₆ ≤ 1500.
B)X₁ + X₂ + X₃ + X₄ + X₅ + X₆ ≥ 1500.
C)10X₁ + 15X₂ + 12X₃ + 18X₄ + 15X₅ + 21X₆ ≤ 1500.
D)10X₁ + 15X₂ + 12X₃ + 18X₄ + 15X₅ + 21X₆ ≥ 1500.
E)X₁ + X₃ + X₅ ≥ 1500.

Question 55

Table 8-6
The following is a linear programming formulation of a labor planning problem.There are four overlapping shifts,and management must decide how many employees to schedule to start work on each shift.The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day.The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
According to Table 8-6,which describes a labor planning problem and its solution,how many workers would be assigned to shift 3?

A)13
B)14
C)16
D)0
E)None of the above

Question 56

Table 8-3
A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education.There are different cost implications for the region of the country where the college is located and the type of degree.The survey cost table is provided below: The requirements for the survey are as follows:
1.The survey must have at least 1500 students
2.At least 400 graduate students
3.At least 100 graduate students should be from the West
4.No more than 500 undergraduate students should be from the East
5.At least 75 graduate students should be from the Central region
6.At least 300 students should be from the West
The marketing research firm would like to minimize the cost of the survey while meeting the requirements.Let X₁ = # of undergraduate students from the East region,X₂ = # of graduate students from the East region,X₃ = # of undergraduate students from the Central region,X₄ = # of graduate students from the Central region,X₅ = # of undergraduate students from the West region,and X₆ = # of graduate students from the West region.
According to Table 8-3,the constraint that there must be at least 400 graduate students is expressed as

A)X₁ + X₂ + X₃ + X₄ + X₅ + X₆ ≥ 400.
B)X₁ + X₂ + X₃ + X₄ + X₅ + X₆ ≤ 400.
C)X₁ + X₃ + X₅ ≥ 400.
D)X₂ + X₄ + X₆ ≥ 400.
E)X₁ + X₂ + X₃ ≥ 400.

Question 57

Table 8-5
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9.Each bookcase yields a $12 profit.Kent's firm is small and its resources limited.During any given production period (of 1 week),10 gallons of varnish and 12 lengths of high quality redwood are available.Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood.Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
T = number of tables produced each week
B = number of bookcases produced each week
Referring to Table 8-5,which of the following constraints would be used?

A)9T + 12B ≤ 12
B)1T + 1B ≥ 10
C)1T + 2B ≤ 12
D)All of the above
E)None of the above

Question 58

Table 8-5
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9.Each bookcase yields a $12 profit.Kent's firm is small and its resources limited.During any given production period (of 1 week),10 gallons of varnish and 12 lengths of high quality redwood are available.Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood.Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
T = number of tables produced each week
B = number of bookcases produced each week
Referring to Table 8-5,if we were to frame this as a linear programming problem,the objective function would be

A)maximize 9B + 12T.
B)maximize 9T + 12B.
C)minimize 10T + 10B.
D)maximize 12T + 10B.
E)None of the above

Question 59

Table 8-5
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9.Each bookcase yields a $12 profit.Kent's firm is small and its resources limited.During any given production period (of 1 week),10 gallons of varnish and 12 lengths of high quality redwood are available.Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood.Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
T = number of tables produced each week
B = number of bookcases produced each week
Referring to Table 8-5,which of the following constraints would be used?

A)10T + 12B ≤ 12
B)1T + 1B ≤ 10
C)1T + 2B ≥ 12
D)All of the above
E)None of the above

Question 60

Table 8-4
A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 4 hours of assembly,3 hours of finishing,and 1 hour of inspection.Each chair requires 3 hours of assembly,2 hours of finishing,and 2 hours of inspection.The selling price per table is $140 while the selling price per chair is $90.Currently,each week there are 220 hours of assembly time available,160 hours of finishing time,and 45 hours of inspection time.Assume that one hour of assembly time costs $5.00;one hour of finishing time costs $6.00;one hour of inspection time costs $4.50;and that whatever labor hours are not required for the table and chairs can be applied to another product.Linear programming is to be used to develop a production schedule.Define the variables as follows:
T = number of tables produced each week
C = number of chairs produced each week
According to Table 8-4,which describes a production problem,what would the objective function be?

A)maximize T + C
B)maximize 140T + 90C
C)minimize 42.5T + 36C
D)maximize 97.5T + 54C
E)maximize 124.5T + 74.5C

Question 61

What are the decision variables in the diet problem?

A)amount of each ingredient to use
B)number of ingredients to use
C)amount of each type of food to purchase
D)number of items of food to purchase
E)None of the above

Question 62

Which of the following statements is false regarding the portfolio selection problem?

A)The typical objective is to maximize the expected return on investment.
B)The constraints only pertain to risk.
C)Typical applications include banks,mutual funds,investment services,and insurance companies.
D)The problem typically includes both greater-than-or-equal-to and less-than-or-equal-to constraints.
E)The problem can also factor in legal requirements.

Question 63

Table 8-7
Ivana Myrocle wishes to invest her inheritance of $200,000 so that her return on investment is maximized,but she also wishes to keep her risk level relatively low.She has decided to invest her money in any of three possible ways: CDs,which pay a guaranteed 6 percent;stocks,which have an expected return of 13 percent;and a money market mutual fund,which is expected to return 8 percent.She has decided that any or all of the $200,000 may be invested,but any part (or all)of it may be put in any of the 3 alternatives.Thus,she may have some money invested in all three alternatives.In formulating this as a linear programming problem,define the variables as follows:
C = dollars invested in CDs
S = dollars invested in stocks
M = dollars invested in the money market mutual fund
According to Table 8-7,which describes an investment problem,which of the following would be the most appropriate constraint in the linear programming problem?

A)0.06C + 0.13S + 0.08M ≤ 200000
B)C + S + M ≥ 200000
C)C + S + M ≤ 200000
D)C + S + M = 200000
E)None of the above

Question 64

What is the objective in the truck loading problem?

A)minimize trucking distance
B)minimize the weight of the load shipped
C)maximize the value of the load shipped
D)minimize the cost of the load shipped
E)None of the above

Question 65

The selection of specific investments from among a wide variety of alternatives is the type of LP problem known as

A)the product mix problem.
B)the investment banker problem.
C)the Wall Street problem.
D)the portfolio selection problem.
E)None of the above

Question 66

A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 3 hours of assembly,2 hours of finishing,and 1 hour of inspection.Each chair requires 2 hours of assembly,2 hours of finishing,and 1 hour of inspection.The profit per table is $120,while the profit per chair is $80.Currently,each week there are 200 hours of assembly time available,180 hours of finishing time,and 40 hours of inspection time.To keep a balance,the number of chairs produced should be at least twice the number of tables.Also,the number of chairs cannot exceed six times the number of tables.Formulate this as a linear programming problem.Carefully define all decision variables.

Question 67

The following problem type is such a special case of linear programming that a special algorithm has been developed to solve it.

A)the production mix problem
B)the diet problem
C)the ingredient mix problem
D)the transportation problem
E)None of the above

Question 68

Table 8-7
Ivana Myrocle wishes to invest her inheritance of $200,000 so that her return on investment is maximized,but she also wishes to keep her risk level relatively low.She has decided to invest her money in any of three possible ways: CDs,which pay a guaranteed 6 percent;stocks,which have an expected return of 13 percent;and a money market mutual fund,which is expected to return 8 percent.She has decided that any or all of the $200,000 may be invested,but any part (or all)of it may be put in any of the 3 alternatives.Thus,she may have some money invested in all three alternatives.In formulating this as a linear programming problem,define the variables as follows:
C = dollars invested in CDs
S = dollars invested in stocks
M = dollars invested in the money market mutual fund
According to Table 8-7,which describes an investment problem,suppose that Ivana has assigned the following risk factors to each investment instrument - CDs (C): 1.2;stocks (S): 4.8;money market mutual fund (M): 3.2.If Ivana decides that she wants the risk factor for the whole investment to be less than 3.3,how should the necessary constraint be written?

A)1.2C + 4.8S + 3.2M ≤ 3.3
B)C + S + M ≤ 3.3
C)1.2C + 4.8S + 3.2M ≤ 3.3(C + S + M)
D)(1.2C + 4.8S + 3.2M)/3 ≤ 3.3
E)S = 0

Question 69

When formulating transportation LP problems,constraints usually deal with the

A)number of items to be transported.
B)shipping cost associated with transporting goods.
C)distance goods are to be transported.
D)number of origins and destinations.
E)capacities of origins and requirements of destinations.

Question 70

Cedar Point amusement park management is preparing the park's annual promotional plan for the coming season.Several advertising alternatives exist: newspaper,television,radio,and displays at recreational shows.The information below shows the characteristics associated with each of the advertising alternatives,as well as the maximum number of placements available in each medium.Given an advertising budget of $250,000,how many placements should be made in each medium to maximize total audience exposure? Formulate this as a linear programming problem.

Question 71

Linear programming is usually used by managers involved in portfolio selection to

A)maximize return on investment.
B)maximize investment limitations.
C)maximize risk.
D)minimize risk.
E)minimize expected return on investment.

Question 72

When formulating transportation LP problems,the objective function usually deals with the

A)number of items to be transported.
B)choice of transportation mode (e.g. ,truck,airplane,railroad,etc. ).
C)shipping cost or distances associated with transporting goods.
D)number of origins and destinations.
E)capacities of origins and requirements of destinations.

Question 73

A computer start-up named Pear is considering entering the U.S.market with what they believe to be a smaller and faster computer than some of the existing products on the market.They want to get a feel for whether or not customers would be willing to switch from some of the existing bigger brands to consider their product.They want to collect a reasonable sample from across the U.S.representative of all age brackets.They have split the United States into 2 regions: East and West.They want at least 65% of their sample to cover the East and no fewer than 25% of the West.They also have divided the age groups into 3 categories: 18-35,36-69,and 70 and up.They want at least 50% of their sample to be between 18-35 and at least 40% to be between 36-69.The costs per person surveyed is given in the table below: Assume that at least 1,000 people are to be surveyed.The problem is for Pear Company to decide how many people to survey from each age bracket within each region in order to minimize costs while meeting requirements.Find the optimal solution and minimum cost.

Question 74

What is the objective in the diet problem?

A)maximize nutrition
B)minimize number of ingredients
C)minimize calories
D)minimize cost
E)None of the above

Question 75

Table 8-7
Ivana Myrocle wishes to invest her inheritance of $200,000 so that her return on investment is maximized,but she also wishes to keep her risk level relatively low.She has decided to invest her money in any of three possible ways: CDs,which pay a guaranteed 6 percent;stocks,which have an expected return of 13 percent;and a money market mutual fund,which is expected to return 8 percent.She has decided that any or all of the $200,000 may be invested,but any part (or all)of it may be put in any of the 3 alternatives.Thus,she may have some money invested in all three alternatives.In formulating this as a linear programming problem,define the variables as follows:
C = dollars invested in CDs
S = dollars invested in stocks
M = dollars invested in the money market mutual fund
According to Table 8-7,which describes an investment problem,suppose that Ivana has decided that the amount invested in stocks cannot exceed one-fourth of the total amount invested.Which is the best way to write this constraint?

A)S ≤ 100,000/4
B)0.13S ≤ 0.24C + 0.32M
C)-C + 4S - M ≤ 0
D)S ≤ (C + M)/ 4
E)-C + 3S - M ≤ 0

Question 76

The shipping problem in LP is also called the

A)production mix problem.
B)freight train problem.
C)transportation problem.
D)land and sea problem.
E)None of the above

Question 77

What is another name for blending problems?

A)diet problems
B)ingredient problems
C)feed mix problems
D)production mix problems
E)media selection problems

Question 78

When applying linear programming to diet problems,the objective function is usually designed to

A)maximize profits from blends of nutrients.
B)maximize ingredient blends.
C)minimize production losses.
D)maximize the number of products to be produced.
E)minimize the costs of nutrient blends.

Question 79

A computer start-up named Pear is considering entering the U.S.market with what they believe to be a smaller and faster computer than some of the existing products on the market.They want to get a feel for whether or not customers would be willing to switch from some of the existing bigger brands to consider their product.They want to collect a reasonable sample from across the U.S.representative of all age brackets.They have split the United States into 2 regions: East and West.They want at least 65% of their sample to cover the East and no fewer than 25% of the West.They also have divided the age groups into 3 categories: 18-35,36-69,and 70 and up.They want at least 50% of their sample to be between 18-35 and at least 40% to be between 36-69.The costs per person surveyed is given in the table below: Assume that at least 1,000 people are to be surveyed.The problem is for Pear Company to decide how many people to survey from each age bracket within each region in order to minimize costs while meeting requirements.Formulate this problem as a linear program.

Question 80

Which of the following statements is true regarding the labor planning problem?

A)It is typically a maximization problem.
B)Required labor hours translate into less-than-or-equal-to constraints.
C)The decision variables can include how many full- and part-time workers to use.
D)The problem is only unique to banks.
E)None of the above