Deck 13: Linear Optimization

Question 1

In the expression 3.0A + 3.5B + 2.3C ≥ 850,where A,B,and C are decision variables of a problem,the constraint function is the ________.

A)contradiction of the inequality given in the expression
B)inequality in the expression
C)left-hand side of the expression
D)right-hand side of the expression

Answer 1

left-hand side of the expression

Question 2

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
Determine the net optimal profit for the given data.

A)$525
B)$1,365
C)$1,890
D)$200

Answer 2

$1,890

Question 3

Use the scenario given below to answer the following question(s).
Ray Inc.manufactures two types of gaming consoles,the sp² hybrid and the sp³ hybrid models.The manufacturing process consists of two principal departments: design and production.The design department has 58 skilled workers,each of whom works 7 hours per day.The production department has 25 workers,who also work a 7-hour shift.On an average,to produce an sp² hybrid,Ray Inc.requires 3.5 labor hours for design and 2 labor hours for production.The sp³ model requires 4 labor hours for design and 1.5 labor hours in production.The company anticipates selling at least 1.5 times as many sp³ models as sp² models.The company operates five days per week and makes a net profit of $130 on the sp² model,and $150 on the sp³ hybrid model.Ray Inc.wants to determine how many of each model should be produced on a weekly basis to maximize net profit.
If the numbers of sp² and sp³ models manufactured by the company in a week are 100 and 150 units respectively,determine the total profit generated by the company in a week.

A)$21,450
B)$54,300
C)$757,500
D)$35,500

Answer 3

$35,500

Question 4

Use the scenario given below to answer the following question(s).
Ray Inc.manufactures two types of gaming consoles,the sp² hybrid and the sp³ hybrid models.The manufacturing process consists of two principal departments: design and production.The design department has 58 skilled workers,each of whom works 7 hours per day.The production department has 25 workers,who also work a 7-hour shift.On an average,to produce an sp² hybrid,Ray Inc.requires 3.5 labor hours for design and 2 labor hours for production.The sp³ model requires 4 labor hours for design and 1.5 labor hours in production.The company anticipates selling at least 1.5 times as many sp³ models as sp² models.The company operates five days per week and makes a net profit of $130 on the sp² model,and $150 on the sp³ hybrid model.Ray Inc.wants to determine how many of each model should be produced on a weekly basis to maximize net profit.
If the numbers of sp² and sp³ hybrid gaming consoles produced each day are denoted as X₁ and X₂ respectively,the function that describes the production department's labor constraint for a week is ________.

A)2X₁ + 1.5X₂ ≥ 875
B)9X₁ + 8X₂ ≤ 3500
C)2X₁ + 1.5X₂ ≤ 875
D)9X₁ + 8X₂ ≥ 3500

Question 5

In linear optimization models,an objective function is the ________.

A)set of values that satisfies all the constraints
B)unknown value that the model seeks to determine
C)quantity that we seek to minimize or maximize
D)limitation or requirement that decision variables must satisfy

Question 6

If the Solver reports that "The Set Cell values do not converge.",the linear optimization model ________.

A)has alternate optimal solutions
B)is infeasible
C)is unbounded
D)has a unique optimal solution

Question 7

The ________ is the difference between the right- and left-hand sides of a constraint.

A)shadow price
B)slack
C)allowable increase
D)optimal solution

Question 8

In linear optimization,the phrase "must contain exactly" specifies a(n)"________" relationship.

A)=
B)≤
C)≥
D)≠

Question 9

Use the scenario given below to answer the following question(s).
Ray Inc.manufactures two types of gaming consoles,the sp² hybrid and the sp³ hybrid models.The manufacturing process consists of two principal departments: design and production.The design department has 58 skilled workers,each of whom works 7 hours per day.The production department has 25 workers,who also work a 7-hour shift.On an average,to produce an sp² hybrid,Ray Inc.requires 3.5 labor hours for design and 2 labor hours for production.The sp³ model requires 4 labor hours for design and 1.5 labor hours in production.The company anticipates selling at least 1.5 times as many sp³ models as sp² models.The company operates five days per week and makes a net profit of $130 on the sp² model,and $150 on the sp³ hybrid model.Ray Inc.wants to determine how many of each model should be produced on a weekly basis to maximize net profit.
If the number of sp² and sp³ models manufactured by the company are 100 and 150 respectively,the number hours used in the design department is ________.

A)950
B)425
C)850
D)580

Question 10

Use the scenario given below to answer the following question(s).
Ray Inc.manufactures two types of gaming consoles,the sp² hybrid and the sp³ hybrid models.The manufacturing process consists of two principal departments: design and production.The design department has 58 skilled workers,each of whom works 7 hours per day.The production department has 25 workers,who also work a 7-hour shift.On an average,to produce an sp² hybrid,Ray Inc.requires 3.5 labor hours for design and 2 labor hours for production.The sp³ model requires 4 labor hours for design and 1.5 labor hours in production.The company anticipates selling at least 1.5 times as many sp³ models as sp² models.The company operates five days per week and makes a net profit of $130 on the sp² model,and $150 on the sp³ hybrid model.Ray Inc.wants to determine how many of each model should be produced on a weekly basis to maximize net profit.
Which of the following is a decision variable in the given problem?

A)sp³ hybrid gaming consoles produced per week
B)total profit that Ray,Inc.wants to maximize
C)the number of workers the firm has
D)the labor hours required to produce the two models

Question 11

The shadow price ________.

A)tells how much the value of the allowable decrease will change as the right-hand side of a constraint is reduced to 0
B)tells how much the value of the allowable increase will change as the left-hand side of a constraint is reduced to 0
C)tells how much the value of the objective function will change as the right-hand side of a constraint is increased by 1
D)tells how much the objective coefficient needs to be reduced in order for a nonnegative variable that is zero in the optimal solution to become positive

Question 12

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
Determine the objective function.

A)Minimize profit = 5.375X₁ + 10.75X₂
B)Minimize profit = 130X₁ + 100X₂
C)Maximize profit = 100X₁ + 130 X₂
D)Maximize profit = 24X₁ + 14X₂

Question 13

A binding constraint is one ________.

A)for which the Cell Value is equal to the right-hand side of the value of the constraint
B)for which the Cell Value is greater than the right-hand side of the value of the constraint
C)for which the Cell Value is lesser than the right-hand side of the value of the constraint
D)for which the Cell Value is not equal to the right-hand side of the value of the constraint

Question 14

In linear optimization,the phrase "cannot exceed" specifies a(n)"________" inequality.

A)>
B)≤
C)≥
D)≠

Question 15

Use the scenario given below to answer the following question(s).
Ray Inc.manufactures two types of gaming consoles,the sp² hybrid and the sp³ hybrid models.The manufacturing process consists of two principal departments: design and production.The design department has 58 skilled workers,each of whom works 7 hours per day.The production department has 25 workers,who also work a 7-hour shift.On an average,to produce an sp² hybrid,Ray Inc.requires 3.5 labor hours for design and 2 labor hours for production.The sp³ model requires 4 labor hours for design and 1.5 labor hours in production.The company anticipates selling at least 1.5 times as many sp³ models as sp² models.The company operates five days per week and makes a net profit of $130 on the sp² model,and $150 on the sp³ hybrid model.Ray Inc.wants to determine how many of each model should be produced on a weekly basis to maximize net profit.
For the given data,identify the objective function.

A)sp³ hybrid models produced/week = 1.5 sp² hybrid models produced/week
B)maximize total profit = 150sp³ models produced/week + 130 sp² models produced/week
C)total labor used in production ≤ 2,030 labor hours
D)3sp³ hybrid models produced/week ≥ sp² hybrid models produced/week

Question 16

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
Calculate the number of swivel chairs produced in a day.

A)10.5 units
B)5.25 units
C)15 units
D)30 units

Question 17

Use the scenario given below to answer the following question(s).
Ray Inc.manufactures two types of gaming consoles,the sp² hybrid and the sp³ hybrid models.The manufacturing process consists of two principal departments: design and production.The design department has 58 skilled workers,each of whom works 7 hours per day.The production department has 25 workers,who also work a 7-hour shift.On an average,to produce an sp² hybrid,Ray Inc.requires 3.5 labor hours for design and 2 labor hours for production.The sp³ model requires 4 labor hours for design and 1.5 labor hours in production.The company anticipates selling at least 1.5 times as many sp³ models as sp² models.The company operates five days per week and makes a net profit of $130 on the sp² model,and $150 on the sp³ hybrid model.Ray Inc.wants to determine how many of each model should be produced on a weekly basis to maximize net profit.
If the numbers of sp² and sp³ hybrid gaming consoles produced each week are denoted as X₁ and X₂ respectively,the function that describes the design department's labor constraint for a week is ________.

A)3.5X₁ + 4X₂ ≥ 2030
B)3.5X₁ + 4X₂ ≤ 2030
C)16X₁ + 14X₂ ≤ 8120
D)16X₁ + 14X₂ ≥ 8120

Question 18

An optimal solution is ________.

A)also known as the constraint function
B)the quantity that we seek to minimize or maximize
C)the limitation or requirement that decision variables must satisfy
D)any set of decision variable values that maximizes or minimizes the objective function

Question 19

Use the scenario given below to answer the following question(s).
Ray Inc.manufactures two types of gaming consoles,the sp² hybrid and the sp³ hybrid models.The manufacturing process consists of two principal departments: design and production.The design department has 58 skilled workers,each of whom works 7 hours per day.The production department has 25 workers,who also work a 7-hour shift.On an average,to produce an sp² hybrid,Ray Inc.requires 3.5 labor hours for design and 2 labor hours for production.The sp³ model requires 4 labor hours for design and 1.5 labor hours in production.The company anticipates selling at least 1.5 times as many sp³ models as sp² models.The company operates five days per week and makes a net profit of $130 on the sp² model,and $150 on the sp³ hybrid model.Ray Inc.wants to determine how many of each model should be produced on a weekly basis to maximize net profit.
Which of the following statements is true of the number of sp³ and sp² hybrids to be manufactured in a week?

A)If the numbers of sp³ and sp² units manufactured per week are 362 and 165 units respectively,the difference between the number of hours used by the design department and the design department's labor time limitation is 30 labor hours/week.
B)If the numbers of sp³ and sp² units manufactured per week are 360 and 160 units respectively,the difference between the production department's labor time limitation and the number of hours used by the production department is 15 labor hours/week.
C)If the numbers of sp³ and sp² units manufactured per week are 360 and 160 units respectively,the number of labor hours used by the design department is 825 labor hours/week.
D)If the numbers of sp³ and sp² units manufactured per week are 355 and 155 units respectively,the number of labor hours used by the production department is 1962.5 labor hours/week.

Question 20

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
Using the data,calculate the number of no-swivel chairs produced in a day.

A)10.5 units
B)5.25 units
C)15 units
D)30 units

Question 21

Use the scenario given below to answer the following question(s).
The Ranger group of industries has a factory that produces three types of action figures,types 1,2,and 3,on a make-to-order basis.The factory operates five days a week for 9 hours each day.The key decision facing the manager is what type of machine should be used to process each action figure during the coming quarter (13 weeks).Two types of machines can be used: captain and regular.Captain machines can be used to make all action figures and are the only machines that can produce certain action figures,such as "The move action figures." Demands,variable costs for each type of machine,and production rates on the machines are given in the table below.
The factory has 30 regular machines and 6 captain machines.After manufacturing,the action figures are sent to the finishing department and then sold.Any action figure that cannot be manufactured in the factory because of limited capacity will be purchased from an external supplier,finished at the factory,and sold at the market selling price.
If C_i,R_i,and P_i (where i = 1,2,3…)are used to denote the number of action figures to be produced on captain machines,the number of action figures to be produced on regular machines,and the number of action figures purchased from an outside supplier respectively,which of the following are the constraints that meet production requirements?

A)C₁ + P₁ = 90,000 C₂+ R₂ + P₂ = 153,000
C₃ + R₃ + P₃ = 20,000
B)R₁ + P₁ = 153,000 C₂+ R₂ + P₂ = 180,000
C₃ + R₃ + P₃ = 40,000
C)R₁ + C₁ = 76,500 C₂+ R₂ + P₂ = 45,000
C₃ + R₃ + P₃ = 10,000
D)R₁ + P₁ = 38,250 C₂+ R₂ + P₂ = 22,500
C₃ + R₃ + P₃ = 5,000

Question 22

Use the scenario given below to answer the following question(s).
The Ranger group of industries has a factory that produces three types of action figures,types 1,2,and 3,on a make-to-order basis.The factory operates five days a week for 9 hours each day.The key decision facing the manager is what type of machine should be used to process each action figure during the coming quarter (13 weeks).Two types of machines can be used: captain and regular.Captain machines can be used to make all action figures and are the only machines that can produce certain action figures,such as "The move action figures." Demands,variable costs for each type of machine,and production rates on the machines are given in the table below.
The factory has 30 regular machines and 6 captain machines.After manufacturing,the action figures are sent to the finishing department and then sold.Any action figure that cannot be manufactured in the factory because of limited capacity will be purchased from an external supplier,finished at the factory,and sold at the market selling price.
If C_i,R_i,and P_i (where i = 1,2,3…)are used to denote the number of a9ction figures to be produced on captain machines,the number of action figures to be produced on regular machines,and the number of action figures purchased from an outside supplier,determine the constraint on available production time on regular machines.

A)0.0962 R₂ + 0.1136 R₃ ≤ 17,550 hours
B)0.0962 R₂ + 0.1136 R₃ ≤ 3,510 hours
C)0.106 R₁ + 0.0962 R₂ + 0.1136 R₃ ≤ 17,550 hours
D)0.769 R₁ + 0.820 R₂ + 1.00 R₃ ≤ 3,510 hours

Question 23

Use the scenario given below to answer the following question(s).
The Ranger group of industries has a factory that produces three types of action figures,types 1,2,and 3,on a make-to-order basis.The factory operates five days a week for 9 hours each day.The key decision facing the manager is what type of machine should be used to process each action figure during the coming quarter (13 weeks).Two types of machines can be used: captain and regular.Captain machines can be used to make all action figures and are the only machines that can produce certain action figures,such as "The move action figures." Demands,variable costs for each type of machine,and production rates on the machines are given in the table below.
The factory has 30 regular machines and 6 captain machines.After manufacturing,the action figures are sent to the finishing department and then sold.Any action figure that cannot be manufactured in the factory because of limited capacity will be purchased from an external supplier,finished at the factory,and sold at the market selling price.
If C_i,R_i,and P_i (where i = 1,2,3…)are used to denote the number of action figures to be produced on captain machines,the number of action figures to be produced on regular machines,and the number of action figures purchased from an outside supplier respectively,determine the objective function for the data given above.

A)Minimize total cost = 9.4 C₁ + 10.4 C₂ + 8.8 C₃ + 10.4 R₂ + 8.8 R₃ + 1.30 P₁ + 1.22 P₂ + 1.00 P₃
B)Minimize total cost = 9.4 C₁ + 10.4 C₂ + 8.8 C₃ + 10.4 R₂ + 8.8 R₃ + 1.70 P₁ + 1.50 P₂ + 1.30 P₃
C)Minimize total cost = 1.22 C₁ + 1.00 C₂ + 1.70 C₃ + 1.22 R₂ + 1.00 R₃ + 1.70 P₁ + 1.50 P₂ + 1.30 P₃
D)Minimize total cost = 1.30 C₁ + 1.22 C₂ + 1.00 C₃ + 1.22 R₂ + 1.00 R₃ + 1.70 P₁ + 1.50 P₂ + 1.30 P₃

Question 24

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
If the limitation in the finishing department is changed to 43 labor hours,the total profit ________.

A)will decrease by $45
B)will increase by $5
C)will decrease by $5
D)will increase by $45

Question 25

Use the data given below to answer the following question(s).
Ball Inc.specializes in producing disinfectants.In developing a new disinfectant,company scientists have specified that the mixture must contain at least 26% hydrogen,at least 30% oxygen,and no more than 28% water.The percentages of each of these constituents in two types of ingredients that can be used to produce the disinfectant are given in the table,along with the wholesale cost per pound.
Let X₁ and X₂ denote DDT and solid carbon dioxide,respectively.
What is the objective function?

A)Maximize profit = 0.52 X₁ + 0.08 X₂
B)Minimize cost = 0.08 X₁ + 0.52 X₂
C)Minimize cost = 3.2 X₁ + 2.4 X₂
D)Minimize cost = 0.44 X₁ + 3.80 X₂

Question 26

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
If an extra finishing hour was used,the company will be able to produce an additional ________ no-swivel chairs.

A)0.25
B)0.5
C)0.125
D)0.225

Question 27

The statement,"The amount invested in online advertising cannot be more than thrice the amount invested in print advertising," is an example of a(n)________.

A)proportional relationship
B)balance constraint
C)allowable decrease
D)allowable increase

Question 28

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
If 7.2 additional hours of finishing time were available,the profit would change by ________.

A)$45
B)$369
C)$324
D)$450

Question 29

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
The optimal values of the decision variables will change if the ________.

A)unit profit for no-swivel chairs either increases by more than 20 or decreases by more than 180
B)unit profit for swivel chairs either increases by more than 80 or decreases by more than 20
C)unit profit for no-swivel chairs either increases by more than 45 or decreases by more than 21
D)unit profit for swivel chairs either increases by more than 45 or decreases by more than 21

Question 30

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
The difference between the right- and left-hand sides of the fabrication labor constraint is ________.

A)5.25 units
B)10.5 units
C)0 units
D)47.25 units

Question 31

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
In which of the following cases is the Cell Value equal to the right-hand side of the value of the constraint?

A)quantity of no-swivel produced
B)quantity of swivel produced
C)fabrication hours used
D)finishing hours used

Question 32

Use the scenario given below to answer the following question(s).
The Ranger group of industries has a factory that produces three types of action figures,types 1,2,and 3,on a make-to-order basis.The factory operates five days a week for 9 hours each day.The key decision facing the manager is what type of machine should be used to process each action figure during the coming quarter (13 weeks).Two types of machines can be used: captain and regular.Captain machines can be used to make all action figures and are the only machines that can produce certain action figures,such as "The move action figures." Demands,variable costs for each type of machine,and production rates on the machines are given in the table below.
The factory has 30 regular machines and 6 captain machines.After manufacturing,the action figures are sent to the finishing department and then sold.Any action figure that cannot be manufactured in the factory because of limited capacity will be purchased from an external supplier,finished at the factory,and sold at the market selling price.
If C_i,R_i,and P_i (where i = 1,2,3…)are used to denote the number of action figures to be produced on captain machines,the number of action figures to be produced on regular machines,and the number of action figures purchased from an outside supplier respectively,determine the constraint on available production time on captain machines.

A)0.0962 R₂ + 0.1136 R₃ ≤ 3,510 hours
B)0.0962 C₂ + 0.114 C₃ ≤ 17,550 hours
C)0.106 C₁ + 0.096 C₂ + 0.114 C₃ ≤ 3,510 hours
D)0.769 C₁ + 0.820 C₂ + 1.00 C₃ ≤ 3,510 hours

Question 33

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
If two workers in the finishing department were ill for a day and could not report to work,the overall profit will reduce by ________.

A)$1,260
B)$315
C)$180
D)$630

Question 34

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
In the finishing constraint,the shadow price of 45 indicates ________.

A)that if there are 45 additional hours of finishing available,then the total profit will change by $1
B)that if an additional hour of finishing time is available,then the total profit will change by $45
C)that if the allowable decrease 42 changes to 41,then the total profit will increase by $45
D)that if the allowable decrease 42 changes to 43,then the total profit will decrease by $45

Question 35

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
The statement,"Production in October plus any available inventory must equal October's demand plus inventory held in November," is an example of a(n)________.

A)proportional relationship
B)balance constraint
C)allowable increase
D)allowable decrease

Question 36

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
If an extra finishing hour was used,the company will be able to produce an additional ________ swivel chairs.

A)0.25
B)0.5
C)0.125
D)0.225

Question 37

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
What is the allowable decrease per unit of swivel chair produced?

A)$120.75
B)$42
C)$47.25
D)$13.33

Question 38

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
In which of the following cases is the Cell Value not equal to the right-hand side of the value of the constraint?

A)total profit
B)profit contribution of swivel chairs
C)fabrication hours used
D)market mixture excess no-swivel

Question 39

Consider the scenario given below.Use Excel solver to answer the following question(s).
Peca Inc.is a small manufacturer of two types of office chairs,the swivel and no-swivel models.The manufacturing process consists of two principal departments: fabrication and finishing.The fabrication department has 24 skilled workers,each of whom works 7 hours per day.The finishing department has 6 workers,who also work a 7-hour shift.A swivel type requires 7 labor hours in the fabricating department and 2 labor hours in finishing.The no-swivel model requires 8 labor hours in fabricating and 3 labor hours in finishing.Peca Inc.makes a net profit of $100 on the swivel model,and $130 on the no-swivel model.The company anticipates selling at least twice as many no-swivel models as swivel models.The company wants to determine how many of each model should be produced on a daily basis to maximize net profit.
If a worker in the finishing department falls ill for a day and is unable to report to work,the overall profit will reduce by ________.

A)$1,260
B)$315
C)$1801
D)$630

Question 40

Use the data given below to answer the following question(s).
Ball Inc.specializes in producing disinfectants.In developing a new disinfectant,company scientists have specified that the mixture must contain at least 26% hydrogen,at least 30% oxygen,and no more than 28% water.The percentages of each of these constituents in two types of ingredients that can be used to produce the disinfectant are given in the table,along with the wholesale cost per pound.
Let X₁ and X₂ denote DDT and solid carbon dioxide,respectively.
The objective of the data given above is to determine the appropriate amount of ingredients to include in one pound of mix.This leads to the constraint ________.

A)X₁ + X₂ = 1
B)X₁ + X₂ < 1
C)X₁ + X₂ > 1
D)X₁ + X₂ ≥ 1

Question 41

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
The total cost incurred by Stoudemire Inc.is ________.(Hint: Use Solver)

A)$31,472
B)$13,472
C)$27,431
D)$43,127

Question 42

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
For the data given above,the objective function is ________.

A)Minimize total cost = 13.60X₁₁ + 15.35X₁₂ + 12.52X₁₃ + 18.58 X₁₄ + 10.75X₂₁ + 17.26X₂₂ + 9.11X₂₃ + 18.92X₂₄
B)Minimize total cost = 15.30X₁₁ + 13.60X₁₂ + 18.58X₁₃ + 12.52X₁₄ + 9.11X₂₁ + 17.26X₂₂ + 450X₂₃ + 18.92X₂₄
C)Maximize total profit = 15.30X₁₁ + 13.60X₁₂ + 18.58X₁₃ + 12.52X₁₄ + 9.11X₂₁ + 17.26X₂₂ + 450X₂₃ + 18.92X₂₄
D)Maximize total profit = 13.60X₁₁ + 15.35X₁₂ + 12.52X₁₃ + 18.58 X₁₄ + 10.75X₂₁ + 17.26X₂₂ + 9.11X₂₃ + 18.92X₂₄

Question 43

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
The number of television sets shipped from the plant in Arkansas to the distribution center in San Antonio is ________.(Hint: Use Solver)

A)450 units
B)300 units
C)100 units
D)950 units

Question 44

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
In which of the following cases is the Cell Value not equal to the right-hand side value of the constraint?

A)total cost
B)total television sets shipped from Arkansas
C)total number of television sets shipped to Miami
D)total number of television sets shipped to Dallas

Question 45

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
Which of the following explains the demand constraint for the distribution center in Miami?

A)X₁₃ + X₂₃ = 450
B)X₁₁ + X₃₃ ≤ 450
C)X₁₃ + X₂₃ ≤ 450
D)X₃₁ + X₃₂ = 450

Question 46

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
Calculate the total number of television sets shipped from the plant in Arizona.(Hint: Use Solver)

A)1400 units
B)1350 units
C)1300 units
D)1250 units

Question 47

Use the data given below to answer the following question(s).
Ball Inc.specializes in producing disinfectants.In developing a new disinfectant,company scientists have specified that the mixture must contain at least 26% hydrogen,at least 30% oxygen,and no more than 28% water.The percentages of each of these constituents in two types of ingredients that can be used to produce the disinfectant are given in the table,along with the wholesale cost per pound.
Let X₁ and X₂ denote DDT and solid carbon dioxide,respectively.
The inequality/equality that describes the oxygen constraint is ________.

A)0.52 X₁ + 0.08 X₂ ≤ 0.26
B)0.52 X₁ + 0.08 X₂ = 0.3
C)0.52 X₁ + 0.08 X₂ ≥ 0.3
D)X₁ < 0

Question 48

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
Determine the equality/inequality that explains the demand constraint for the distribution center in San Antonio.

A)X₁₁ + X₂₁ = 100
B)X₁₁ + X₂₂ ≤ 100
C)X₁₁ + X₂₂ ≥ 100
D)X₁₁ + X₁₂ = 100

Question 49

Use the data given below to answer the following question(s).
Ball Inc.specializes in producing disinfectants.In developing a new disinfectant,company scientists have specified that the mixture must contain at least 26% hydrogen,at least 30% oxygen,and no more than 28% water.The percentages of each of these constituents in two types of ingredients that can be used to produce the disinfectant are given in the table,along with the wholesale cost per pound.
Let X₁ and X₂ denote DDT and solid carbon dioxide,respectively.
The inequality/equality that describes the water constraint is ________.

A)0.166 X₁ + 0.151 X₂ ≤ 0.28
B)0.151 X₁ + 0.166 X₂ ≤ 0.28
C)0.166 X₁ + 0.151 X₂ ≥ 0.28
D)X₁ < 0

Question 50

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
The inequality/equality that explains the capacity constraint for the Arkansas plant is ________.

A)X₁₁ + X₂₁ + X₃₁ + X₄₁ = 1000
B)X₁₁ + X₂₁ + X₃₁ + X₄₁ ≥ 1000
C)X₁₂ + X₂₂ + X₃₂ + X₄₂ ≥ 1000
D)X₂₁ + X₂₂ + X₂₃ + X₂₄ ≤ 1000

Question 51

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
Determine the equality/inequality that explains the demand constraint for the distribution center in Washington.

A)X₂₁ + X₂₂ ≥ 300
B)X₁₁ + X₂₂ ≤ 300
C)X₁₂ + X₂₂ = 300
D)X₁₁ + X₁₂ = 300

Question 52

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
Determine the equality/inequality that explains the demand constraint for the distribution center in Dallas.

A)X₁₄ + X₂₄ = 950
B)X₄₁ + X₄₂ = 950
C)X₁₁ + X₄₄ ≥ 950
D)X₄₁ + X₄₂ ≤ 450

Question 53

Use the data given below to answer the following question(s).
Ball Inc.specializes in producing disinfectants.In developing a new disinfectant,company scientists have specified that the mixture must contain at least 26% hydrogen,at least 30% oxygen,and no more than 28% water.The percentages of each of these constituents in two types of ingredients that can be used to produce the disinfectant are given in the table,along with the wholesale cost per pound.
Let X₁ and X₂ denote DDT and solid carbon dioxide,respectively.
Identify the inequality that describes the hydrogen constraint.

A)0.329 X₁ + 0.24 X₂ ≤ 0.26
B)0.329 X₁ + 0.24 X₂ ≥ 0.26
C)0.329 X₁ + 0.24 X₂ ≠ 0.26
D)X₁ > 0

Question 54

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
The inequality/equality that explains the capacity constraint for Arizona is ________.

A)15.30X₁₁ + 13.60X₁₂ + 18.58X₁₃ + 12.52X₁₄ = 1300
B)X₁₁ + X₂₁ + X₃₁ + X₄₁ ≥ 1300
C)X₁₁ + X₁₂ + X₁₃ + X₁₄ ≤ 1300
D)15.30X₁₁ + 13.60X₁₂ + 18.58X₁₃ + 12.52X₁₄ ≥ 1300

Question 55

Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Which of the following is the inequality/equality that describes the time constraint of the forming department?

A)A/50 + B/40 + C/20 + D/20 ≥ 330
B)A/50 + B/40 + C/20 + D/20 ≤ 330
C)A/30 + B/40 + C/20 + D/20 = 330
D)A/50 + B/40 + C/20 + D/20 = 330

Question 56

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
The number of television sets shipped from the plant in Arizona to the distribution center in Washington is ________.(Hint: Use Solver)

A)450 units
B)300 units
C)100 units
D)950 units

Question 57

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
The number of television sets shipped from the plant in Arkansas to the distribution center in Miami is ________.(Hint: Use Solver)

A)450 units
B)300 units
C)100 units
D)950 units

Question 58

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
Calculate the total number of television sets shipped from the plant in Arkansas.(Hint: Use Solver)

A)1400 units
B)1350 units
C)550 units
D)1250 units

Question 59

Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
For the data given above,the objective function is ________.

A)Maximize = 260A + 310B + 410C + 660D
B)Maximize = 220A + 250B + 310C + 530D
C)Maximize = 40A + 60B + 100C + 130D
D)Minimize = 130A + 100B + 60C + 40D

Question 60

Use the case below to answer the following question(s).
Stoudemire Inc.produces televisions at two plants: Arizona and Arkansas.They ship them to major distribution centers in San Antonio,Washington,Miami,and Dallas.The table shown below provides the unit cost of shipping between any plant and distribution center,plant capacities over the next planning period,and distribution center demands.Stoudemire's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Assume X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Arizona,i = 2 represents Arkansas,j = 1 represents San Antonio,j = 2 represents Washington,and so on.
The number of television sets shipped from the plant in Arizona to the distribution center in Dallas is ________.(Hint: Use Solver)

A)450 units
B)300 units
C)100 units
D)950 units

Question 61

Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Which of the following is the inequality/equality that describes the time constraint of the painting department?

A)A/30 + B/30 + C/35 + D/25 ≤ 330
B)B/30 + C/20 + D/20 = 330
C)A/70 + B/50 + C/50 + D/44 = 330
D)A/60 + B/60 + C/70 + D/50 ≤ 330

Question 62

Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Determine the optimal profit contribution of the C-type steel sheets.(Hint: Use Solver)

A)$39,000
B)$390,000
C)$200,000
D)$20,000

Question 63

Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Which of the following is the inequality/equality that describes the time constraint of the sintering department?

A)B/15 + C/10 + D/10 = 330
B)B/30 + C/20 + D/20 = 330
C)A/70 + B/50 + C/50 + D/44 ≥ 330
D)A/35 + B/25 + C/25 + D/22 ≤ 330

Question 64

S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Using Solver,determine the number of hours used in the painting department.

A)175.076 hours
B)302.294 hours
C)225.000 hours
D)320.000 hours

Question 65

A nonbinding constraint is one for which the Cell Value is equal to the right-hand side of the value of the constraint.

Question 66

S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Using Solver,determine the number of hours used in the rolling department.

A)175.076 hours
B)302.294 hours
C)225.000 hours
D)330.000 hours

Question 67

A model is unbounded if Solver reports "The Set Cell values do not converge."

Question 68

Decision variables are the unknown values that the model seeks to determine.

Question 69

Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Using Solver,determine the number of hours used in the forming department.

A)175.076 hours
B)302.294 hours
C)225.000 hours
D)275.091 hours

Question 70

The slack on a binding constraint will always be zero.

Question 71

Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Determine the optimal number of D-type steel sheets produced.(Hint: Use Solver)

A)3,000 units
B)2,000 units
C)500 units
D)1,000 units

Question 72

A problem is unbounded if the objective can be increased or decreased without bound.

Question 73

Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Which of the following is the inequality/equality that describes the time constraint of the rolling department?

A)B/15 + C/10 + D/10 ≥ 330
B)B/30 + C/20 + D/20 ≤ 330
C)B/45 + C/30 + D/30 = 330
D)B/60 + C/40 + D/40 = 330

Question 74

Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Determine the optimal number of B-type steel sheets produced.(Hint: Use Solver)

A)3,000 units
B)2,000 units
C)500 units
D)1,000 units

Question 75

S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Using Solver,determine the total optimal profit generated by S&N Manufacturing.

A)$225,272.73
B)$390,000.00
C)$835,272.73
D)$1,390,000.00

Question 76

S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Using Solver,determine the number of hours used in the quality check department.

A)175.076 hours
B)302.294 hours
C)225.000 hours
D)320.000 hours

Question 77

In the inequality 3x + 4y ≤ 45,the right-hand side is the constraint function.

Question 78

Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Determine the optimal number of C-type steel sheets produced.(Hint: Use Solver)

A)3,000 units
B)2,000 units
C)500 units
D)1,000 units

Question 79

Slack variables are always nonnegative.

Question 80

Use the case below to answer the following question(s).
S&N Manufacturing makes four different steel sheets,A,B,C,and D,with different percentages of iron.Each sheet must flow through five departments,forming,rolling,sintering,painting,and quality check.The table below shows the relevant data.Production rates are shown in units/hour.(Sheet A uses imported steel and does not require rolling.) S&N wants to determine the number of steel sheets to produce in order to maximize monthly profit.
Let A,B,C,and D denote the number of units of model A,B,C,and D to be produced,respectively.
Determine the optimal number of A-type steel sheets produced.(Hint: Use Solver)

A)approximately 7,755 units
B)approximately 5,555 units
C)approximately 3,755 units
D)approximately 2,755 units