Deck 14: Applications of Linear Optimization

Question 1

Problem statements such as the amount of material used in production cannot exceed the amount available in inventory would be categorized as a ________ constraint.

A)proportional relationships
B)limitations
C)requirements
D)simple bounds

Answer 1

B

Question 2

Use the table below to answer the following question(s).
Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis.The mill operates on a 24/7 basis.The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill.Two types of looms are used: Jaquard and Northrop.Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids.Demands, variable costs for each fabric, and production rates on the looms are given in the table below.The mill has 10 Northrop looms and 2 Jaquard looms.Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price.In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally.

Answer the following questions using a linear optimization model.
According to the model, what is the total amount of Fabric 3 to be purchased?

A)2,405
B)0
C)32,595
D)35,000

Answer 2

A

Question 3

Use the table below to answer the following question(s).
Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis.The mill operates on a 24/7 basis.The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill.Two types of looms are used: Jaquard and Northrop.Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids.Demands, variable costs for each fabric, and production rates on the looms are given in the table below.The mill has 10 Northrop looms and 2 Jaquard looms.Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price.In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally.

Answer the following questions using a linear optimization model.
According to the model, what is the total amount of Fabric 1 to be produced on Jaquard?

A)50,000
B)0
C)27,420.8
D)22,579.2

Answer 3

D

Question 4

Which of the following would be considered as an example of a proportional relationships constraint?

A)making certain that only a certain amount of units are produced
B)guaranteeing that a certain amount of workforce will be available for a certain month
C)balancing the input to the output during production
D)ensuring that the budget allocated to marketing is thrice that of research and development

Question 5

Use the table below to answer the following question(s).
Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis.The mill operates on a 24/7 basis.The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill.Two types of looms are used: Jaquard and Northrop.Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids.Demands, variable costs for each fabric, and production rates on the looms are given in the table below.The mill has 10 Northrop looms and 2 Jaquard looms.Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price.In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally.

Answer the following questions using a linear optimization model.
From the Sensitivity Report, what amount (cost/hour)would make it feasible to purchase Fabric 2 rather than produce it?

A)$0.6
B)$0.25
C)$0.128
D)$1.1

Question 6

Use the table below to answer the following question(s).
Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis.The mill operates on a 24/7 basis.The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill.Two types of looms are used: Jaquard and Northrop.Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids.Demands, variable costs for each fabric, and production rates on the looms are given in the table below.The mill has 10 Northrop looms and 2 Jaquard looms.Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price.In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally.

Answer the following questions using a linear optimization model.
According to the model, what is the total amount of Fabric 2 to be produced with Northrop?

A)0
B)62,000
C)20,160
D)32,595

Question 7

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
Which of the following is the constraint for total amount shipped from Dallas?

A)X₁₁ + X₁₂ + X₁₃ + X₁₄ ≤ 1,250
B)X₂₁ + X₂₂ + X₂₃ + X₂₄ ≤ 1,250
C)X₂₁ + X₂₂ + X₂₃ + X₂₄ ≤ 750
D)X₁₁ + X₁₂ + X₁₃ + X₁₄ - X₂₁ + X₂₂ + X₂₃ + X₂₄ ≤ 850

Question 8

Use the table below to answer the following question(s).
Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis.The mill operates on a 24/7 basis.The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill.Two types of looms are used: Jaquard and Northrop.Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids.Demands, variable costs for each fabric, and production rates on the looms are given in the table below.The mill has 10 Northrop looms and 2 Jaquard looms.Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price.In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally.

Answer the following questions using a linear optimization model.
From the Sensitivity Report, which of the following would reduce the total cost by $1.568 for each additional hour of capacity for the Jaquard looms?

A)decreasing the Northrop loom cost per hour by $0.58
B)decreasing the Northrop loom capacity down by 534.4
C)increasing the Jaquard loom capacity up by 4896.5 hours
D)increasing the Jaquard loom capacity up by 4032 hours

Question 9

Use the table below to answer the following question(s).
Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis.The mill operates on a 24/7 basis.The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill.Two types of looms are used: Jaquard and Northrop.Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids.Demands, variable costs for each fabric, and production rates on the looms are given in the table below.The mill has 10 Northrop looms and 2 Jaquard looms.Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price.In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally.

Answer the following questions using a linear optimization model.
According to the model, what is the total amount of Fabric 1 to be purchased?

A)27,420.8
B)50,000
C)22,579.2
D)32,595

Question 10

________ constraints essentially state that input = output and ensure that the flow of material or money is accounted for at locations or between time periods.

A)Requirements
B)Proportional relationships
C)Balance
D)Limitations

Question 11

Use the table below to answer the following question(s).
Qualis Investments is a private limited business that manages personal financial portfolios.The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance.Characteristics of the funds are given in the table below.

The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund.The total amount invested in the low-priced and multinational funds are at least 35% of the total investment.The client would like an average return of at least 6%.Assume that through represents the dollar amount invested in funds 1 through 6, respectively.
Which of the following is the objective function minimize total risk?

A)11.87 X₁ + 12.62 X₂ + 13.72 .X₃ + 3.37 X₄ + 8.4 X₅ + 6.91 X₆
B)7)23 X₁ + 8.42 X₂ + 6.66 .X₃ + 2.72 X₄ + 8.89 X₅ + 3.5 X₆
C)11.87 X₁ + 12.62 X₂ + 13.72 .X₃ + 3.37 X₄ + 8.4 X₅ + 6.91 X₆ / ₇₅₀,₀₀₀
D)7)23 X₁ + 8.42 X₂ + 6.66 .X₃ + 2.72 X₄ + 8.89 X₅ + 3.5 X₆ ≥ ₆%

Question 12

Problem statements such as production must be sufficient to meet promised customer orders would be categorized as a ________ constraint.

A)limitations
B)requirements
C)proportional relationships
D)balance

Question 13

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
Which of the following is the objective function for cost minimization?

A)minimize cost = 13 X₁₁ +15.25 X₁₂ +10.99 X₁₃ +18.48 X₁₄ / 10.75 X₂₁ +15.16 X₂₂ +9.65 X₂₃ +18.5 X₂₄
B)minimize cost = 13 X₁₁ +15.25 X₁₂ +10.99 X₁₃ +18.48 X₁₄ + 10.75 X₂₁ +15.16 X₂₂ +9.65 X₂₃ +18.5 X₂₄
C)minimize cost = 13 X₁₁ +15.25 X₁₂ +10.99 X₁₃ +18.48 X₁₄ - 10.75 X₂₁ +15.16 X₂₂ +9.65 X₂₃ +18.5 X₂₄
D)minimize cost = (13 X₁₁ +15.25 X₁₂ +10.99 X₁₃ +18.48 X₁₄ - 10.75 X₂₁ +15.16 X₂₂ +9.65 X₂₃ +18.5 X₂₄ ) (1,250 / 750)

Question 14

Use the table below to answer the following question(s).
Qualis Investments is a private limited business that manages personal financial portfolios.The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance.Characteristics of the funds are given in the table below.

The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund.The total amount invested in the low-priced and multinational funds are at least 35% of the total investment.The client would like an average return of at least 6%.Assume that through represents the dollar amount invested in funds 1 through 6, respectively.
Which of the following is the constraint for the weighted return?

A)X₁ + X₂ + X₃ + X₄ + X₅ + X₆ = 750,000
B)7)23 X₁ + 8.42 X₂ + 6.66 .X₃ + 2.72 X₄ + 8.89 X₅ + 3.5 X₆ ≥ ₆.₀₀
C)7)23 X₁ + 8.42 X₂ + 6.66 .X₃ + 2.72 X₄ + 8.89 X₅ + 3.5 X₆ / ₇₅₀,₀₀₀ ≥ ₆.₀₀
D)7)23 X₁ + 8.42 X₂ + 6.66 .X₃ + 2.72 X₄ + 8.89 X₅ + 3.5 X₆ / 750,000

Question 15

Which of the following is an example of a simple bounds constraint?

A)confirming that production does not go beyond a certain unit value
B)reducing production due to scarcity of resources
C)meeting targets for a specific sales job
D)equaling production in September with the resources available at the end of August

Question 16

Use the table below to answer the following question(s).
Qualis Investments is a private limited business that manages personal financial portfolios.The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance.Characteristics of the funds are given in the table below.

The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund.The total amount invested in the low-priced and multinational funds are at least 35% of the total investment.The client would like an average return of at least 6%.Assume that through represents the dollar amount invested in funds 1 through 6, respectively.
Which of the following describes the constraint on the mid-cap fund?

A)X₃ ≥ 0.35(750,000)
B)X₃ ≥ 80,000
C)X₃ ≥ 0.35(80,000)
D)X₃ ≤ 670,000

Question 17

Use the table below to answer the following question(s).
Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis.The mill operates on a 24/7 basis.The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill.Two types of looms are used: Jaquard and Northrop.Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids.Demands, variable costs for each fabric, and production rates on the looms are given in the table below.The mill has 10 Northrop looms and 2 Jaquard looms.Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price.In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally.

Answer the following questions using a linear optimization model.
According to the model, what is the total amount of Fabric 3 to be produced with Northrop?

A)0
B)35,000
C)2,405
D)32,595

Question 18

Use the table below to answer the following question(s).
Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis.The mill operates on a 24/7 basis.The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill.Two types of looms are used: Jaquard and Northrop.Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids.Demands, variable costs for each fabric, and production rates on the looms are given in the table below.The mill has 10 Northrop looms and 2 Jaquard looms.Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price.In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally.

Answer the following questions using a linear optimization model.
According to the model, what is the total amount of Fabric 2 to be purchased?

A)50,000
B)62,000
C)0
D)2,405

Question 19

Use the table below to answer the following question(s).
Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis.The mill operates on a 24/7 basis.The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill.Two types of looms are used: Jaquard and Northrop.Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids.Demands, variable costs for each fabric, and production rates on the looms are given in the table below.The mill has 10 Northrop looms and 2 Jaquard looms.Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price.In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally.

Answer the following questions using a linear optimization model.
According to the model, what is the total cost incurred by Remington for producing the three fabrics?

A)$96,540.47
B)$149,240.47
C)$96,227.82
D)$88,862.65

Question 20

Use the table below to answer the following question(s).
Qualis Investments is a private limited business that manages personal financial portfolios.The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance.Characteristics of the funds are given in the table below.

The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund.The total amount invested in the low-priced and multinational funds are at least 35% of the total investment.The client would like an average return of at least 6%.Assume that through represents the dollar amount invested in funds 1 through 6, respectively.
Which of the following is the constraint for investment in low-priced and multinational funds?

A)X₁ + X₂ ≥ 0.35(750,000)
B) ≥ 0.35(750,000)
C)X₁ + X₂ + X₃ + X₄ + X₅ + X₆ ≥ 0.35(750,000)
D) ≥ 0.35

Question 21

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
According to the transportation model, what is the amount shipped from Atlanta to Jacksonville?

A)950
B)480
C)0
D)95

Question 22

Use the table below to answer the following question(s).
Letherin Hides is a company that makes boots specifically targeting college students.Forecasts of sales for the next year are 200 in the summer, 450 in the autumn, and 500 in the winter.Accessories that are used on the boots are purchased from a supplier for $31.66.The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the holding cost per item is 0.06($31.66)= $1.9 per quarter (rounded figure).Letherin Hides hires freelance art designers at part-time to craft designs during the summer, and they earn $6 per hour.In the autumn, labor is more difficult to keep, and the owner must pay $6.5 per hour to retain qualified help.Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and workers earn $7.75 per hour.Each boot design takes 2 hours to complete.How should production be planned over the three quarters to minimize the combined production and inventory holding costs?
The table below provides information on Letherin Hides boot design cost and production.

Use a linear optimization model based on the data to answer the following questions.
According to the linear optimization model, what is the inventory held at the end of autumn?

A)0
B)200
C)950
D)500

Question 23

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
According to the Sensitivity report on the model, by what price should the unit cost of shipment reduce to make shipment from Dallas to Houston feasible?

A)$8.68
B)$2.16
C)$10.84
D)$3.41

Question 24

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
According to the transportation model, what is the total cost incurred by Riviera Transport Company?

A)$29,016.95
B)$26,698.95
C)$20,331.35
D)$41,978.75

Question 25

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
In a sensitivity report, a solution is considered a(n)________ solution if the right-hand-side value of any constraint has a zero Allowable Increase or Allowable Decrease.

A)algorithmic
B)unbounded
C)infeasible
D)degenerate

Question 26

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
From the Sensitivity Report on the model, to which of the following cities can Atlanta not ship to without reducing unit cost of production?

A)Houston
B)San Jose
C)Jacksonville
D)Memphis

Question 27

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
Based on the Sensitivity Report on the model, which of the following is the savings on a reduction of demand of 2 units at Jacksonville?

A)$2.5
B)$1.25
C)$19.48
D)$16.98

Question 28

Use the table below to answer the following question(s).
Letherin Hides is a company that makes boots specifically targeting college students.Forecasts of sales for the next year are 200 in the summer, 450 in the autumn, and 500 in the winter.Accessories that are used on the boots are purchased from a supplier for $31.66.The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the holding cost per item is 0.06($31.66)= $1.9 per quarter (rounded figure).Letherin Hides hires freelance art designers at part-time to craft designs during the summer, and they earn $6 per hour.In the autumn, labor is more difficult to keep, and the owner must pay $6.5 per hour to retain qualified help.Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and workers earn $7.75 per hour.Each boot design takes 2 hours to complete.How should production be planned over the three quarters to minimize the combined production and inventory holding costs?
The table below provides information on Letherin Hides boot design cost and production.

Use a linear optimization model based on the data to answer the following questions.
According to the linear optimization model, what is the total amount to be produced in summer?

A)200
B)100
C)550
D)0

Question 29

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
According to the transportation model, what is the total shipment from Dallas?

A)750
B)1,180
C)430
D)950

Question 30

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
According to the transportation model, which of the following is the amount shipped from Dallas to San Jose?

A)0
B)95
C)230
D)325

Question 31

Use the table below to answer the following question(s).
Letherin Hides is a company that makes boots specifically targeting college students.Forecasts of sales for the next year are 200 in the summer, 450 in the autumn, and 500 in the winter.Accessories that are used on the boots are purchased from a supplier for $31.66.The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the holding cost per item is 0.06($31.66)= $1.9 per quarter (rounded figure).Letherin Hides hires freelance art designers at part-time to craft designs during the summer, and they earn $6 per hour.In the autumn, labor is more difficult to keep, and the owner must pay $6.5 per hour to retain qualified help.Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and workers earn $7.75 per hour.Each boot design takes 2 hours to complete.How should production be planned over the three quarters to minimize the combined production and inventory holding costs?
The table below provides information on Letherin Hides boot design cost and production.

Use a linear optimization model based on the data to answer the following questions.
According to the linear optimization model, what is the total cost incurred by Letherin Hides for the combined seasons?

A)$17,075
B)$15,605
C)$15,700
D)$18,700

Question 32

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
According to the transportation model, what is the amount shipped from Atlanta to Memphis?

A)480
B)0
C)230
D)950

Question 33

Use the table below to answer the following question(s).
Letherin Hides is a company that makes boots specifically targeting college students.Forecasts of sales for the next year are 200 in the summer, 450 in the autumn, and 500 in the winter.Accessories that are used on the boots are purchased from a supplier for $31.66.The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the holding cost per item is 0.06($31.66)= $1.9 per quarter (rounded figure).Letherin Hides hires freelance art designers at part-time to craft designs during the summer, and they earn $6 per hour.In the autumn, labor is more difficult to keep, and the owner must pay $6.5 per hour to retain qualified help.Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and workers earn $7.75 per hour.Each boot design takes 2 hours to complete.How should production be planned over the three quarters to minimize the combined production and inventory holding costs?
The table below provides information on Letherin Hides boot design cost and production.

Use a linear optimization model based on the data to answer the following questions.
According to the linear optimization model, what is the inventory held at the end of summer?

A)450
B)0
C)200
D)550

Question 34

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
According to the transportation model, which of the following is the amount shipped from Dallas to Houston?

A)0
B)175
C)1,180
D)750

Question 35

Use the table below to answer the following question(s).
Letherin Hides is a company that makes boots specifically targeting college students.Forecasts of sales for the next year are 200 in the summer, 450 in the autumn, and 500 in the winter.Accessories that are used on the boots are purchased from a supplier for $31.66.The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the holding cost per item is 0.06($31.66)= $1.9 per quarter (rounded figure).Letherin Hides hires freelance art designers at part-time to craft designs during the summer, and they earn $6 per hour.In the autumn, labor is more difficult to keep, and the owner must pay $6.5 per hour to retain qualified help.Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and workers earn $7.75 per hour.Each boot design takes 2 hours to complete.How should production be planned over the three quarters to minimize the combined production and inventory holding costs?
The table below provides information on Letherin Hides boot design cost and production.

Use a linear optimization model based on the data to answer the following questions.
According to the linear optimization model, what is the net production for autumn?

A)200
B)500
C)450
D)50

Question 36

Use the table below to answer the following question(s).
Letherin Hides is a company that makes boots specifically targeting college students.Forecasts of sales for the next year are 200 in the summer, 450 in the autumn, and 500 in the winter.Accessories that are used on the boots are purchased from a supplier for $31.66.The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the holding cost per item is 0.06($31.66)= $1.9 per quarter (rounded figure).Letherin Hides hires freelance art designers at part-time to craft designs during the summer, and they earn $6 per hour.In the autumn, labor is more difficult to keep, and the owner must pay $6.5 per hour to retain qualified help.Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and workers earn $7.75 per hour.Each boot design takes 2 hours to complete.How should production be planned over the three quarters to minimize the combined production and inventory holding costs?
The table below provides information on Letherin Hides boot design cost and production.

Use a linear optimization model based on the data to answer the following questions.
According to the linear optimization model, what is the net production for winter?

A)0
B)950
C)200
D)500

Question 37

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
Which of the following gives the constraint for the demand met at a distribution center?

A)X₁₁ + X₂₁ = 1,250
B)X₁₃ + X₂₃ ≥ 210
C)X₁₃ + X₂₃ = 770
D)X₁₃ + X₂₃ = 480

Question 38

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
Which of the following is the constraint of nonnegativity for all values of i and j?

A)13 X₁₁ +15.25 X₁₂ +10.99 X₁₃ +18.48 X₁₄ / 10.75 X₂₁ +15.16 X₂₂ + 9.65 X₂₃ +18.5 X₂₄ ≤ 0
B)Xᵢⱼ ≥ 0, for all i and j
C)Xᵢⱼ ≤ 0, for all i and j
D)

Question 39

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
Which of the following is the constraint for total amount shipped from Atlanta?

A)X₁₁ + X₁₂ + X₁₃ + X₁₄ - X₂₁ + X₂₂ + X₂₃ + X₂₄ ≤ 850
B)X₂₁ + X₂₂ + X₂₃ + X₂₄ ≤ 750
C)X₂₁ + X₂₂ + X₂₃ + X₂₄ ≤ 1250
D)X₁₁ + X₁₂ + X₁₃ + X₁₄ ≤ 1250

Question 40

Use the table below to answer the following question(s).
The Riviera Transport Company (RTC)produces car accessories at two plants: Dallas and Atlanta.They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis.The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands.RTC'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 Xᵢⱼ = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.
Answer the following question(s)using a linear optimization model.
According to the Sensitivity Report, which of the following is true if the capacity at Atlanta is increased by 230 units?

A)the total cost can be reduced by $.09 per unit
B)the total cost at Atlanta increases by $9
C)the total cost per unit will reduce by $.09 to Memphis
D)the shadow price at Atlanta will increase to $0.09

Question 41

Keychain Publishing is planning to release two books, simultaneously, by the same author.One is a fictional book, while the other is the author's autobiography.The details of its cost, production, and demand are given in the table below.

Keychain Publishing has $150,000 available to bind books and advertise them with an objective of maximizing profit contribution.Provide the objective function for maximizing profits, along with its constraints.

Question 42

Degeneracy does not impact the interpretation of sensitivity analysis information.

Question 43

Linear optimization cannot be used on problems having multiple time periods.

Question 44

Give an account of balance constraints with some examples of verbal clues.

Question 45

Nonnegativity of the decision variables is an example of an explicit constraint.

Question 46

Use the table below to answer the following question(s).
Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen.Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging.The table below shows the relevant data.Production rates are shown in units/hour.(ScarCT is assembled elsewhere).Pickson wants to determine how many guitars to make to maximize monthly profit.

Use a linear optimization model based on the data to answer the following question.
According to the linear optimization model, what would be the total time spent for packaging the Invazen models?

A)8
B)16
C)20
D)10

Question 47

Use the table below to answer the following question(s).
Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen.Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging.The table below shows the relevant data.Production rates are shown in units/hour.(ScarCT is assembled elsewhere).Pickson wants to determine how many guitars to make to maximize monthly profit.

Use a linear optimization model based on the data to answer the following question.
According to the linear optimization model, what would be the total time spent for sound testing the Warax model?

A)5
B)4
C)6
D)10.5

Question 48

List out the different types of constraints that help model formulation.

Question 49

Use the table below to answer the following question(s).
Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen.Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging.The table below shows the relevant data.Production rates are shown in units/hour.(ScarCT is assembled elsewhere).Pickson wants to determine how many guitars to make to maximize monthly profit.

Use a linear optimization model based on the data to answer the following question.
According to the linear optimization model, what would be the total time spent for assembling the Invazen models?

A)8
B)4
C)16
D)10

Question 50

Use the table below to answer the following question(s).
Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen.Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging.The table below shows the relevant data.Production rates are shown in units/hour.(ScarCT is assembled elsewhere).Pickson wants to determine how many guitars to make to maximize monthly profit.

Use a linear optimization model based on the data to answer the following question.
According to the linear optimization model, what is the total hours spent for painting all the models?

A)220
B)94.94
C)109.67
D)199.44

Question 51

Use the table below to answer the following question(s).
Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen.Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging.The table below shows the relevant data.Production rates are shown in units/hour.(ScarCT is assembled elsewhere).Pickson wants to determine how many guitars to make to maximize monthly profit.

Use a linear optimization model based on the data to answer the following question.
According to the linear optimization model, what is the total number of ScarCTs produced?

A)2500
B)750
C)0
D)100

Question 52

Use the table below to answer the following question(s).
Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen.Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging.The table below shows the relevant data.Production rates are shown in units/hour.(ScarCT is assembled elsewhere).Pickson wants to determine how many guitars to make to maximize monthly profit.

Use a linear optimization model based on the data to answer the following question.
According to the linear optimization model, what is the net profit per unit on Dela Mort?

A)$205,200
B)$108
C)$680
D)$90

Question 53

Use the table below to answer the following question(s).
Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen.Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging.The table below shows the relevant data.Production rates are shown in units/hour.(ScarCT is assembled elsewhere).Pickson wants to determine how many guitars to make to maximize monthly profit.

Use a linear optimization model based on the data to answer the following question.
According to the Sensitivity Report, by how much should the unit profit on ScarCT be reduced in order for its production to be feasible?

A)$30
B)$90
C)$60
D)$120

Question 54

Use the table below to answer the following question(s).
Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen.Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging.The table below shows the relevant data.Production rates are shown in units/hour.(ScarCT is assembled elsewhere).Pickson wants to determine how many guitars to make to maximize monthly profit.

Use a linear optimization model based on the data to answer the following question.
According to the linear optimization model, which of the following departments uses all the time that it is allocated to finish its job?

A)assembly
B)painting
C)inspection
D)packaging

Question 55

The mathematical form Y ≤ 450 would be considered as representing a simple bounds constraint.

Question 56

Use the table below to answer the following question(s).
Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen.Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging.The table below shows the relevant data.Production rates are shown in units/hour.(ScarCT is assembled elsewhere).Pickson wants to determine how many guitars to make to maximize monthly profit.

Use a linear optimization model based on the data to answer the following question.
According to the linear optimization model, what would be the total time spent on inspecting the Dela Mort models?

A)158.33
B)12.5
C)85
D)48

Question 57

Use the table below to answer the following question(s).
Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen.Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging.The table below shows the relevant data.Production rates are shown in units/hour.(ScarCT is assembled elsewhere).Pickson wants to determine how many guitars to make to maximize monthly profit.

Use a linear optimization model based on the data to answer the following question.
According to the linear optimization model, what is the total profit contribution by the Invazen model?

A)$205,200
B)$20,000
C)$10,000
D)$4,000

Question 58

What is degeneracy in linear optimization? Give an example.

Question 59

When interpreting sensitivity analysis information for changes in model parameters, all other model parameters are held constant.

Question 60

Use the table below to answer the following question(s).
Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen.Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging.The table below shows the relevant data.Production rates are shown in units/hour.(ScarCT is assembled elsewhere).Pickson wants to determine how many guitars to make to maximize monthly profit.

Use a linear optimization model based on the data to answer the following question.
According to the linear optimization model, what is the total profit for the Pickson Luthiers Corporation?

A)$10,000
B)$199,880
C)$205,200
D)$219,200

Question 61

How does Solver handle simple lower bounds and upper bounds compared to ordinary constraints?

Question 62

How does Excel's Solver help interpret reduced cost as shadow price for bounded variables?