Deck 15: Optimization Analytics

Question 1

Use the table below to answer the following questions).
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. $$\begin{array} { | c | l | c | c | } \hline & \text { Qualis Mutual Fund Data } & & \\\hline & & \begin{array} { c } \text { Expected Annual } \\\text { Return }\end{array} &\text { Risk Measure } \\\hline 1 & \text { Qualis Low-priced Stock Fund } & 7.23 \% & 11.87 \\\hline 2 & \text { Qualis Multinational Fund } & 8.42 \% & 12.62 \\\hline 3 & \text { Qualis Mid-cap Stock Fund } & 6.66 \% & 13.72 \\\hline 4 & \text { Qualis Mortgage Fund } & 2.72 \% & 3.37 \\\hline 5 & \text { Qualis Income Equity Fund } & 8.89 \% & 8.4 \\\hline 6 & \text { Qualis Balanced Fund } & 3.50 \% & 6.91 \\\hline \end{array}$$ 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 X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively.

-If the unit profit on both Graystone and Lava surfboards is increased by $10, what is the shadow price for the finishing hours used?

A) -4.35
B) 8.33
C) 20.65
D) 32.46

Answer 1

20.65

Question 2

Use the table below to answer the following questions).
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. $$\begin{array} { | c | l | c | c | } \hline & \text { Qualis Mutual Fund Data } & & \\\hline & & \begin{array} { c } \text { Expected Annual } \\\text { Return }\end{array} &\text { Risk Measure } \\\hline 1 & \text { Qualis Low-priced Stock Fund } & 7.23 \% & 11.87 \\\hline 2 & \text { Qualis Multinational Fund } & 8.42 \% & 12.62 \\\hline 3 & \text { Qualis Mid-cap Stock Fund } & 6.66 \% & 13.72 \\\hline 4 & \text { Qualis Mortgage Fund } & 2.72 \% & 3.37 \\\hline 5 & \text { Qualis Income Equity Fund } & 8.89 \% & 8.4 \\\hline 6 & \text { Qualis Balanced Fund } & 3.50 \% & 6.91 \\\hline \end{array}$$ 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 X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively.

-If the unit profit on Graystone surfboards is increased by $10, what is the total profit generated?

A) $ 489.13
B) $ 521.74
C) $ 423.91
D) $ 554.35

Answer 2

$ 554.35

Question 3

Use the table below to answer the following questions).
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. $\begin{array}{|l|l|l|l|l|l|}\hline\text { Remington } & & & \\\text { Textiles } & & & \\\hline & & & &\\\hline \text { Data }\\\hline \text { Fabric } & \text { Demand } & \text { Jaquard } & \text { Northrop } \\&&\text { Capacity } & \text { Capacity } & \text { Mill Cost } & \text { Outsourcing } \\&\text { yards) } & \text { yards/hour) } & \text { yards/hour) } & \text { \$/yard) } & \text { Cost \$/yard) }\\\hline 1 & 50,000 & 5.6 & 0 & 0.53 & 0.81 \\\hline 2 & 62,000 & 5.2 & 4.8 & 0.6 & 0.85 \\\hline 3 & 35,000 & 4.8 & 4.5 & 0.71 & 0.84 \\\hline\end{array}$ 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

Answer 3

27,420.8

Question 4

Use the table below to answer the following questions).
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. $$\begin{array} { | c | l | c | c | } \hline & \text { Qualis Mutual Fund Data } & & \\\hline & & \begin{array} { c } \text { Expected Annual } \\\text { Return }\end{array} &\text { Risk Measure } \\\hline 1 & \text { Qualis Low-priced Stock Fund } & 7.23 \% & 11.87 \\\hline 2 & \text { Qualis Multinational Fund } & 8.42 \% & 12.62 \\\hline 3 & \text { Qualis Mid-cap Stock Fund } & 6.66 \% & 13.72 \\\hline 4 & \text { Qualis Mortgage Fund } & 2.72 \% & 3.37 \\\hline 5 & \text { Qualis Income Equity Fund } & 8.89 \% & 8.4 \\\hline 6 & \text { Qualis Balanced Fund } & 3.50 \% & 6.91 \\\hline \end{array}$$ 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 X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively.

-If the unit profit on Graystone surfboards is increased by $10, what is the Allowable Increase for Lava surfboards?

A) 30.00
B) 85.00
C) 16.67
D) 58.75

Question 5

Use the table below to answer the following questions).
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. $\begin{array}{|l|l|l|l|l|l|}\hline\text { Remington } & & & \\\text { Textiles } & & & \\\hline & & & &\\\hline \text { Data }\\\hline \text { Fabric } & \text { Demand } & \text { Jaquard } & \text { Northrop } \\&&\text { Capacity } & \text { Capacity } & \text { Mill Cost } & \text { Outsourcing } \\&\text { yards) } & \text { yards/hour) } & \text { yards/hour) } & \text { \$/yard) } & \text { Cost \$/yard) }\\\hline 1 & 50,000 & 5.6 & 0 & 0.53 & 0.81 \\\hline 2 & 62,000 & 5.2 & 4.8 & 0.6 & 0.85 \\\hline 3 & 35,000 & 4.8 & 4.5 & 0.71 & 0.84 \\\hline\end{array}$ 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 6

Use the table below to answer the following questions).
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. $$\begin{array} { | c | l | c | c | } \hline & \text { Qualis Mutual Fund Data } & & \\\hline & & \begin{array} { c } \text { Expected Annual } \\\text { Return }\end{array} &\text { Risk Measure } \\\hline 1 & \text { Qualis Low-priced Stock Fund } & 7.23 \% & 11.87 \\\hline 2 & \text { Qualis Multinational Fund } & 8.42 \% & 12.62 \\\hline 3 & \text { Qualis Mid-cap Stock Fund } & 6.66 \% & 13.72 \\\hline 4 & \text { Qualis Mortgage Fund } & 2.72 \% & 3.37 \\\hline 5 & \text { Qualis Income Equity Fund } & 8.89 \% & 8.4 \\\hline 6 & \text { Qualis Balanced Fund } & 3.50 \% & 6.91 \\\hline \end{array}$$ 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 X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively.

-If the unit profit on both Graystone and Lava surfboards is increased by $10, what is the total profit generated?

A) $ 521.74
B) $ 505.43
C) $ 423.91
D) $ 619.57

Question 7

Whenever a constraint has positive slack, the shadow price is equal to one.

Question 8

Use the table below to answer the following questions).
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. $\begin{array}{|l|l|l|l|l|l|}\hline\text { Remington } & & & \\\text { Textiles } & & & \\\hline & & & &\\\hline \text { Data }\\\hline \text { Fabric } & \text { Demand } & \text { Jaquard } & \text { Northrop } \\&&\text { Capacity } & \text { Capacity } & \text { Mill Cost } & \text { Outsourcing } \\&\text { yards) } & \text { yards/hour) } & \text { yards/hour) } & \text { \$/yard) } & \text { Cost \$/yard) }\\\hline 1 & 50,000 & 5.6 & 0 & 0.53 & 0.81 \\\hline 2 & 62,000 & 5.2 & 4.8 & 0.6 & 0.85 \\\hline 3 & 35,000 & 4.8 & 4.5 & 0.71 & 0.84 \\\hline\end{array}$ 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

Question 9

Use the table below to answer the following questions).
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. $\begin{array}{|l|l|l|l|l|l|}\hline\text { Remington } & & & \\\text { Textiles } & & & \\\hline & & & &\\\hline \text { Data }\\\hline \text { Fabric } & \text { Demand } & \text { Jaquard } & \text { Northrop } \\&&\text { Capacity } & \text { Capacity } & \text { Mill Cost } & \text { Outsourcing } \\&\text { yards) } & \text { yards/hour) } & \text { yards/hour) } & \text { \$/yard) } & \text { Cost \$/yard) }\\\hline 1 & 50,000 & 5.6 & 0 & 0.53 & 0.81 \\\hline 2 & 62,000 & 5.2 & 4.8 & 0.6 & 0.85 \\\hline 3 & 35,000 & 4.8 & 4.5 & 0.71 & 0.84 \\\hline\end{array}$ 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 10

The indicates how much the value of the objective function will change as the right- hand side of a constraint is increased by 1.

A) objective coefficient
B) shadow price
C) binding constraint
D) reduced cost

Question 11

Use the table below to answer the following questions).
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. $$\begin{array} { | c | l | c | c | } \hline & \text { Qualis Mutual Fund Data } & & \\\hline & & \begin{array} { c } \text { Expected Annual } \\\text { Return }\end{array} &\text { Risk Measure } \\\hline 1 & \text { Qualis Low-priced Stock Fund } & 7.23 \% & 11.87 \\\hline 2 & \text { Qualis Multinational Fund } & 8.42 \% & 12.62 \\\hline 3 & \text { Qualis Mid-cap Stock Fund } & 6.66 \% & 13.72 \\\hline 4 & \text { Qualis Mortgage Fund } & 2.72 \% & 3.37 \\\hline 5 & \text { Qualis Income Equity Fund } & 8.89 \% & 8.4 \\\hline 6 & \text { Qualis Balanced Fund } & 3.50 \% & 6.91 \\\hline \end{array}$$ 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 X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively.

-If the unit profit on both Graystone and Lava surfboards is increased by $10, what is the Allowable Decrease for Lava surfboards?

A) 95.00
B) 38.46
C) 20.00
D) 11.11

Question 12

Use the table below to answer the following questions).
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. $\begin{array}{|l|l|l|l|l|l|}\hline\text { Remington } & & & \\\text { Textiles } & & & \\\hline & & & &\\\hline \text { Data }\\\hline \text { Fabric } & \text { Demand } & \text { Jaquard } & \text { Northrop } \\&&\text { Capacity } & \text { Capacity } & \text { Mill Cost } & \text { Outsourcing } \\&\text { yards) } & \text { yards/hour) } & \text { yards/hour) } & \text { \$/yard) } & \text { Cost \$/yard) }\\\hline 1 & 50,000 & 5.6 & 0 & 0.53 & 0.81 \\\hline 2 & 62,000 & 5.2 & 4.8 & 0.6 & 0.85 \\\hline 3 & 35,000 & 4.8 & 4.5 & 0.71 & 0.84 \\\hline\end{array}$ 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 13

Use the table below to answer the following questions).
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. $\begin{array}{|l|l|l|l|l|l|}\hline\text { Remington } & & & \\\text { Textiles } & & & \\\hline & & & &\\\hline \text { Data }\\\hline \text { Fabric } & \text { Demand } & \text { Jaquard } & \text { Northrop } \\&&\text { Capacity } & \text { Capacity } & \text { Mill Cost } & \text { Outsourcing } \\&\text { yards) } & \text { yards/hour) } & \text { yards/hour) } & \text { \$/yard) } & \text { Cost \$/yard) }\\\hline 1 & 50,000 & 5.6 & 0 & 0.53 & 0.81 \\\hline 2 & 62,000 & 5.2 & 4.8 & 0.6 & 0.85 \\\hline 3 & 35,000 & 4.8 & 4.5 & 0.71 & 0.84 \\\hline\end{array}$ 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 14

Use the table below to answer the following questions).
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. $\begin{array}{|l|l|l|l|l|l|}\hline\text { Remington } & & & \\\text { Textiles } & & & \\\hline & & & &\\\hline \text { Data }\\\hline \text { Fabric } & \text { Demand } & \text { Jaquard } & \text { Northrop } \\&&\text { Capacity } & \text { Capacity } & \text { Mill Cost } & \text { Outsourcing } \\&\text { yards) } & \text { yards/hour) } & \text { yards/hour) } & \text { \$/yard) } & \text { Cost \$/yard) }\\\hline 1 & 50,000 & 5.6 & 0 & 0.53 & 0.81 \\\hline 2 & 62,000 & 5.2 & 4.8 & 0.6 & 0.85 \\\hline 3 & 35,000 & 4.8 & 4.5 & 0.71 & 0.84 \\\hline\end{array}$ Answer the following questions using a linear optimization model.

-From the Sensitivity Report, what cost reduction $/hour) would make it feasible to purchase some amount of Fabric 2 from the external supplier rather than just produce it?

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

Question 15

Use the table below to answer the following questions).
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. $\begin{array}{|l|l|l|l|l|l|}\hline\text { Remington } & & & \\\text { Textiles } & & & \\\hline & & & &\\\hline \text { Data }\\\hline \text { Fabric } & \text { Demand } & \text { Jaquard } & \text { Northrop } \\&&\text { Capacity } & \text { Capacity } & \text { Mill Cost } & \text { Outsourcing } \\&\text { yards) } & \text { yards/hour) } & \text { yards/hour) } & \text { \$/yard) } & \text { Cost \$/yard) }\\\hline 1 & 50,000 & 5.6 & 0 & 0.53 & 0.81 \\\hline 2 & 62,000 & 5.2 & 4.8 & 0.6 & 0.85 \\\hline 3 & 35,000 & 4.8 & 4.5 & 0.71 & 0.84 \\\hline\end{array}$ 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 16

Use the table below to answer the following questions).
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. $$\begin{array} { | c | l | c | c | } \hline & \text { Qualis Mutual Fund Data } & & \\\hline & & \begin{array} { c } \text { Expected Annual } \\\text { Return }\end{array} &\text { Risk Measure } \\\hline 1 & \text { Qualis Low-priced Stock Fund } & 7.23 \% & 11.87 \\\hline 2 & \text { Qualis Multinational Fund } & 8.42 \% & 12.62 \\\hline 3 & \text { Qualis Mid-cap Stock Fund } & 6.66 \% & 13.72 \\\hline 4 & \text { Qualis Mortgage Fund } & 2.72 \% & 3.37 \\\hline 5 & \text { Qualis Income Equity Fund } & 8.89 \% & 8.4 \\\hline 6 & \text { Qualis Balanced Fund } & 3.50 \% & 6.91 \\\hline \end{array}$$ 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 X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively.

-Due to decreasing profits, if the production of Graystone surfboards is stopped, compute the total profit the firm can earn.

A) $ 521.74
B) $ 489.13
C) $ 423.91
D) $ 500.00

Question 17

Use the table below to answer the following questions).
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. $$\begin{array} { | c | l | c | c | } \hline & \text { Qualis Mutual Fund Data } & & \\\hline & & \begin{array} { c } \text { Expected Annual } \\\text { Return }\end{array} &\text { Risk Measure } \\\hline 1 & \text { Qualis Low-priced Stock Fund } & 7.23 \% & 11.87 \\\hline 2 & \text { Qualis Multinational Fund } & 8.42 \% & 12.62 \\\hline 3 & \text { Qualis Mid-cap Stock Fund } & 6.66 \% & 13.72 \\\hline 4 & \text { Qualis Mortgage Fund } & 2.72 \% & 3.37 \\\hline 5 & \text { Qualis Income Equity Fund } & 8.89 \% & 8.4 \\\hline 6 & \text { Qualis Balanced Fund } & 3.50 \% & 6.91 \\\hline \end{array}$$ 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 X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively.

-If the unit profit on Graystone surfboards is increased by $10, what is the Allowable Decrease for Lava surfboards?

A) 30.00
B) 85.00
C) 16.67
D) 58.75

Question 18

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transportation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) 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 19

Use the table below to answer the following questions).
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. $\begin{array}{|l|l|l|l|l|l|}\hline\text { Remington } & & & \\\text { Textiles } & & & \\\hline & & & &\\\hline \text { Data }\\\hline \text { Fabric } & \text { Demand } & \text { Jaquard } & \text { Northrop } \\&&\text { Capacity } & \text { Capacity } & \text { Mill Cost } & \text { Outsourcing } \\&\text { yards) } & \text { yards/hour) } & \text { yards/hour) } & \text { \$/yard) } & \text { Cost \$/yard) }\\\hline 1 & 50,000 & 5.6 & 0 & 0.53 & 0.81 \\\hline 2 & 62,000 & 5.2 & 4.8 & 0.6 & 0.85 \\\hline 3 & 35,000 & 4.8 & 4.5 & 0.71 & 0.84 \\\hline\end{array}$ 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

Question 20

Use the table below to answer the following questions).
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. $$\begin{array} { | c | l | c | c | } \hline & \text { Qualis Mutual Fund Data } & & \\\hline & & \begin{array} { c } \text { Expected Annual } \\\text { Return }\end{array} &\text { Risk Measure } \\\hline 1 & \text { Qualis Low-priced Stock Fund } & 7.23 \% & 11.87 \\\hline 2 & \text { Qualis Multinational Fund } & 8.42 \% & 12.62 \\\hline 3 & \text { Qualis Mid-cap Stock Fund } & 6.66 \% & 13.72 \\\hline 4 & \text { Qualis Mortgage Fund } & 2.72 \% & 3.37 \\\hline 5 & \text { Qualis Income Equity Fund } & 8.89 \% & 8.4 \\\hline 6 & \text { Qualis Balanced Fund } & 3.50 \% & 6.91 \\\hline \end{array}$$ 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 X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively.

-If the unit profit on Graystone surfboards is increased by $10, what is the shadow price for the finishing hours used?

A) $ 18.48
B) $ 17.39
C) $ 15.42
D) $ 14.15

Question 21

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transportation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) 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 22

Use the table below to answer the following questions).
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. $\begin{array} { |l|l|l|l|l|l| } \hline \begin{array} { l } \text {Pickson Luthiers }\\ \text {Corporation }\\\end{array}\\\hline\\\hline \text {Data}\\\hline \text { Guitar Model } & \begin{array}{l}\text { Selling } \\\text { price/Unit }\end{array} & \begin{array}{l}\text { Variable } \\\text { cost/Unit }\end{array} & \text { Min Sales } & \text { Max Sales } \\\hline \text { ScarCT } & 750.00 & 660.00 & 0 & 2500 \\\hline \text { Dela Mort } & 788.00 & 680.00 & 0 & 2000 \\\hline \text { Warax } & 800.00 & 700.00 & 100 & 1000 \\\hline \text { Invazen } & 850.00 & 800.00 & 80 & 500 \\\hline\\\hline \begin{array}{l}\text { Production rates } \\\text { units/hour) }\end{array} & \text { ScarCT } & \text { Dela Mort } & \text { Warax } & \text { Invazen } & \begin{array}{l}\text { Hours } \\\text { Available }\end{array} \\\hline \text { Assembly } & - & 35 & 25 & 20 & 220 \\\hline \text { Painting } & 35 & 20 & 15 & 10 & 220 \\\hline \text { Sound Testing } & 20 & 10 & 20 & 18 & 220 \\\hline \text { Inspection } & 10 & 12 & 8 & 5 & 220 \\\hline \text { Packaging } & 9 & 10 & 5 & 8 & 220\\\hline\end{array}$
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 23

Use the table below to answer the following questions).
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. $\begin{array} { |l|l|l|l|l|l| } \hline \begin{array} { l } \text {Pickson Luthiers }\\ \text {Corporation }\\\end{array}\\\hline\\\hline \text {Data}\\\hline \text { Guitar Model } & \begin{array}{l}\text { Selling } \\\text { price/Unit }\end{array} & \begin{array}{l}\text { Variable } \\\text { cost/Unit }\end{array} & \text { Min Sales } & \text { Max Sales } \\\hline \text { ScarCT } & 750.00 & 660.00 & 0 & 2500 \\\hline \text { Dela Mort } & 788.00 & 680.00 & 0 & 2000 \\\hline \text { Warax } & 800.00 & 700.00 & 100 & 1000 \\\hline \text { Invazen } & 850.00 & 800.00 & 80 & 500 \\\hline\\\hline \begin{array}{l}\text { Production rates } \\\text { units/hour) }\end{array} & \text { ScarCT } & \text { Dela Mort } & \text { Warax } & \text { Invazen } & \begin{array}{l}\text { Hours } \\\text { Available }\end{array} \\\hline \text { Assembly } & - & 35 & 25 & 20 & 220 \\\hline \text { Painting } & 35 & 20 & 15 & 10 & 220 \\\hline \text { Sound Testing } & 20 & 10 & 20 & 18 & 220 \\\hline \text { Inspection } & 10 & 12 & 8 & 5 & 220 \\\hline \text { Packaging } & 9 & 10 & 5 & 8 & 220\\\hline\end{array}$
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 24

Degeneracy does not impact the interpretation of sensitivity analysis information.

Question 25

Use the table below to answer the following questions).
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. $\begin{array} { |l|l|l|l|l|l| } \hline \begin{array} { l } \text {Pickson Luthiers }\\ \text {Corporation }\\\end{array}\\\hline\\\hline \text {Data}\\\hline \text { Guitar Model } & \begin{array}{l}\text { Selling } \\\text { price/Unit }\end{array} & \begin{array}{l}\text { Variable } \\\text { cost/Unit }\end{array} & \text { Min Sales } & \text { Max Sales } \\\hline \text { ScarCT } & 750.00 & 660.00 & 0 & 2500 \\\hline \text { Dela Mort } & 788.00 & 680.00 & 0 & 2000 \\\hline \text { Warax } & 800.00 & 700.00 & 100 & 1000 \\\hline \text { Invazen } & 850.00 & 800.00 & 80 & 500 \\\hline\\\hline \begin{array}{l}\text { Production rates } \\\text { units/hour) }\end{array} & \text { ScarCT } & \text { Dela Mort } & \text { Warax } & \text { Invazen } & \begin{array}{l}\text { Hours } \\\text { Available }\end{array} \\\hline \text { Assembly } & - & 35 & 25 & 20 & 220 \\\hline \text { Painting } & 35 & 20 & 15 & 10 & 220 \\\hline \text { Sound Testing } & 20 & 10 & 20 & 18 & 220 \\\hline \text { Inspection } & 10 & 12 & 8 & 5 & 220 \\\hline \text { Packaging } & 9 & 10 & 5 & 8 & 220\\\hline\end{array}$
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 26

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transportation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) 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 27

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transportation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) 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 28

Use the table below to answer the following questions).
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. $\begin{array} { |l|l|l|l|l|l| } \hline \begin{array} { l } \text {Pickson Luthiers }\\ \text {Corporation }\\\end{array}\\\hline\\\hline \text {Data}\\\hline \text { Guitar Model } & \begin{array}{l}\text { Selling } \\\text { price/Unit }\end{array} & \begin{array}{l}\text { Variable } \\\text { cost/Unit }\end{array} & \text { Min Sales } & \text { Max Sales } \\\hline \text { ScarCT } & 750.00 & 660.00 & 0 & 2500 \\\hline \text { Dela Mort } & 788.00 & 680.00 & 0 & 2000 \\\hline \text { Warax } & 800.00 & 700.00 & 100 & 1000 \\\hline \text { Invazen } & 850.00 & 800.00 & 80 & 500 \\\hline\\\hline \begin{array}{l}\text { Production rates } \\\text { units/hour) }\end{array} & \text { ScarCT } & \text { Dela Mort } & \text { Warax } & \text { Invazen } & \begin{array}{l}\text { Hours } \\\text { Available }\end{array} \\\hline \text { Assembly } & - & 35 & 25 & 20 & 220 \\\hline \text { Painting } & 35 & 20 & 15 & 10 & 220 \\\hline \text { Sound Testing } & 20 & 10 & 20 & 18 & 220 \\\hline \text { Inspection } & 10 & 12 & 8 & 5 & 220 \\\hline \text { Packaging } & 9 & 10 & 5 & 8 & 220\\\hline\end{array}$
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 29

Use the table below to answer the following questions).
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. $\begin{array} { |l|l|l|l|l|l| } \hline \begin{array} { l } \text {Pickson Luthiers }\\ \text {Corporation }\\\end{array}\\\hline\\\hline \text {Data}\\\hline \text { Guitar Model } & \begin{array}{l}\text { Selling } \\\text { price/Unit }\end{array} & \begin{array}{l}\text { Variable } \\\text { cost/Unit }\end{array} & \text { Min Sales } & \text { Max Sales } \\\hline \text { ScarCT } & 750.00 & 660.00 & 0 & 2500 \\\hline \text { Dela Mort } & 788.00 & 680.00 & 0 & 2000 \\\hline \text { Warax } & 800.00 & 700.00 & 100 & 1000 \\\hline \text { Invazen } & 850.00 & 800.00 & 80 & 500 \\\hline\\\hline \begin{array}{l}\text { Production rates } \\\text { units/hour) }\end{array} & \text { ScarCT } & \text { Dela Mort } & \text { Warax } & \text { Invazen } & \begin{array}{l}\text { Hours } \\\text { Available }\end{array} \\\hline \text { Assembly } & - & 35 & 25 & 20 & 220 \\\hline \text { Painting } & 35 & 20 & 15 & 10 & 220 \\\hline \text { Sound Testing } & 20 & 10 & 20 & 18 & 220 \\\hline \text { Inspection } & 10 & 12 & 8 & 5 & 220 \\\hline \text { Packaging } & 9 & 10 & 5 & 8 & 220\\\hline\end{array}$
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 30

Use the table below to answer the following questions).
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. $\begin{array} { |l|l|l|l|l|l| } \hline \begin{array} { l } \text {Pickson Luthiers }\\ \text {Corporation }\\\end{array}\\\hline\\\hline \text {Data}\\\hline \text { Guitar Model } & \begin{array}{l}\text { Selling } \\\text { price/Unit }\end{array} & \begin{array}{l}\text { Variable } \\\text { cost/Unit }\end{array} & \text { Min Sales } & \text { Max Sales } \\\hline \text { ScarCT } & 750.00 & 660.00 & 0 & 2500 \\\hline \text { Dela Mort } & 788.00 & 680.00 & 0 & 2000 \\\hline \text { Warax } & 800.00 & 700.00 & 100 & 1000 \\\hline \text { Invazen } & 850.00 & 800.00 & 80 & 500 \\\hline\\\hline \begin{array}{l}\text { Production rates } \\\text { units/hour) }\end{array} & \text { ScarCT } & \text { Dela Mort } & \text { Warax } & \text { Invazen } & \begin{array}{l}\text { Hours } \\\text { Available }\end{array} \\\hline \text { Assembly } & - & 35 & 25 & 20 & 220 \\\hline \text { Painting } & 35 & 20 & 15 & 10 & 220 \\\hline \text { Sound Testing } & 20 & 10 & 20 & 18 & 220 \\\hline \text { Inspection } & 10 & 12 & 8 & 5 & 220 \\\hline \text { Packaging } & 9 & 10 & 5 & 8 & 220\\\hline\end{array}$
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 31

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 32

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transportation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) 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 33

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transportation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) 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 34

Use the table below to answer the following questions).
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. $\begin{array} { |l|l|l|l|l|l| } \hline \begin{array} { l } \text {Pickson Luthiers }\\ \text {Corporation }\\\end{array}\\\hline\\\hline \text {Data}\\\hline \text { Guitar Model } & \begin{array}{l}\text { Selling } \\\text { price/Unit }\end{array} & \begin{array}{l}\text { Variable } \\\text { cost/Unit }\end{array} & \text { Min Sales } & \text { Max Sales } \\\hline \text { ScarCT } & 750.00 & 660.00 & 0 & 2500 \\\hline \text { Dela Mort } & 788.00 & 680.00 & 0 & 2000 \\\hline \text { Warax } & 800.00 & 700.00 & 100 & 1000 \\\hline \text { Invazen } & 850.00 & 800.00 & 80 & 500 \\\hline\\\hline \begin{array}{l}\text { Production rates } \\\text { units/hour) }\end{array} & \text { ScarCT } & \text { Dela Mort } & \text { Warax } & \text { Invazen } & \begin{array}{l}\text { Hours } \\\text { Available }\end{array} \\\hline \text { Assembly } & - & 35 & 25 & 20 & 220 \\\hline \text { Painting } & 35 & 20 & 15 & 10 & 220 \\\hline \text { Sound Testing } & 20 & 10 & 20 & 18 & 220 \\\hline \text { Inspection } & 10 & 12 & 8 & 5 & 220 \\\hline \text { Packaging } & 9 & 10 & 5 & 8 & 220\\\hline\end{array}$
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 35

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

Question 36

Use the table below to answer the following questions).
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. $\begin{array} { |l|l|l|l|l|l| } \hline \begin{array} { l } \text {Pickson Luthiers }\\ \text {Corporation }\\\end{array}\\\hline\\\hline \text {Data}\\\hline \text { Guitar Model } & \begin{array}{l}\text { Selling } \\\text { price/Unit }\end{array} & \begin{array}{l}\text { Variable } \\\text { cost/Unit }\end{array} & \text { Min Sales } & \text { Max Sales } \\\hline \text { ScarCT } & 750.00 & 660.00 & 0 & 2500 \\\hline \text { Dela Mort } & 788.00 & 680.00 & 0 & 2000 \\\hline \text { Warax } & 800.00 & 700.00 & 100 & 1000 \\\hline \text { Invazen } & 850.00 & 800.00 & 80 & 500 \\\hline\\\hline \begin{array}{l}\text { Production rates } \\\text { units/hour) }\end{array} & \text { ScarCT } & \text { Dela Mort } & \text { Warax } & \text { Invazen } & \begin{array}{l}\text { Hours } \\\text { Available }\end{array} \\\hline \text { Assembly } & - & 35 & 25 & 20 & 220 \\\hline \text { Painting } & 35 & 20 & 15 & 10 & 220 \\\hline \text { Sound Testing } & 20 & 10 & 20 & 18 & 220 \\\hline \text { Inspection } & 10 & 12 & 8 & 5 & 220 \\\hline \text { Packaging } & 9 & 10 & 5 & 8 & 220\\\hline\end{array}$
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 37

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transportation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) 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 38

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transportation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) 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 39

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transportation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) 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 40

In a sensitivity report, a solution is considered an) 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 41

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

Question 42

Use the table below to answer the following questions).
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. $\begin{array} { |l|l|l|l|l|l| } \hline \begin{array} { l } \text {Pickson Luthiers }\\ \text {Corporation }\\\end{array}\\\hline\\\hline \text {Data}\\\hline \text { Guitar Model } & \begin{array}{l}\text { Selling } \\\text { price/Unit }\end{array} & \begin{array}{l}\text { Variable } \\\text { cost/Unit }\end{array} & \text { Min Sales } & \text { Max Sales } \\\hline \text { ScarCT } & 750.00 & 660.00 & 0 & 2500 \\\hline \text { Dela Mort } & 788.00 & 680.00 & 0 & 2000 \\\hline \text { Warax } & 800.00 & 700.00 & 100 & 1000 \\\hline \text { Invazen } & 850.00 & 800.00 & 80 & 500 \\\hline\\\hline \begin{array}{l}\text { Production rates } \\\text { units/hour) }\end{array} & \text { ScarCT } & \text { Dela Mort } & \text { Warax } & \text { Invazen } & \begin{array}{l}\text { Hours } \\\text { Available }\end{array} \\\hline \text { Assembly } & - & 35 & 25 & 20 & 220 \\\hline \text { Painting } & 35 & 20 & 15 & 10 & 220 \\\hline \text { Sound Testing } & 20 & 10 & 20 & 18 & 220 \\\hline \text { Inspection } & 10 & 12 & 8 & 5 & 220 \\\hline \text { Packaging } & 9 & 10 & 5 & 8 & 220\\\hline\end{array}$
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 increased in order for its production to be feasible?

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

Question 43

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

Question 44

Use the table below to answer the following questions).
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. $\begin{array} { |l|l|l|l|l|l| } \hline \begin{array} { l } \text {Pickson Luthiers }\\ \text {Corporation }\\\end{array}\\\hline\\\hline \text {Data}\\\hline \text { Guitar Model } & \begin{array}{l}\text { Selling } \\\text { price/Unit }\end{array} & \begin{array}{l}\text { Variable } \\\text { cost/Unit }\end{array} & \text { Min Sales } & \text { Max Sales } \\\hline \text { ScarCT } & 750.00 & 660.00 & 0 & 2500 \\\hline \text { Dela Mort } & 788.00 & 680.00 & 0 & 2000 \\\hline \text { Warax } & 800.00 & 700.00 & 100 & 1000 \\\hline \text { Invazen } & 850.00 & 800.00 & 80 & 500 \\\hline\\\hline \begin{array}{l}\text { Production rates } \\\text { units/hour) }\end{array} & \text { ScarCT } & \text { Dela Mort } & \text { Warax } & \text { Invazen } & \begin{array}{l}\text { Hours } \\\text { Available }\end{array} \\\hline \text { Assembly } & - & 35 & 25 & 20 & 220 \\\hline \text { Painting } & 35 & 20 & 15 & 10 & 220 \\\hline \text { Sound Testing } & 20 & 10 & 20 & 18 & 220 \\\hline \text { Inspection } & 10 & 12 & 8 & 5 & 220 \\\hline \text { Packaging } & 9 & 10 & 5 & 8 & 220\\\hline\end{array}$
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 45

For nonlinear models, the Lagrange multipliers are only approximate indicators of shadow prices.

Question 46

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

Question 47

What is degeneracy in linear optimization? Give an example.

Question 48

Use the table below to answer the following questions).
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. $\begin{array} { |l|l|l|l|l|l| } \hline \begin{array} { l } \text {Pickson Luthiers }\\ \text {Corporation }\\\end{array}\\\hline\\\hline \text {Data}\\\hline \text { Guitar Model } & \begin{array}{l}\text { Selling } \\\text { price/Unit }\end{array} & \begin{array}{l}\text { Variable } \\\text { cost/Unit }\end{array} & \text { Min Sales } & \text { Max Sales } \\\hline \text { ScarCT } & 750.00 & 660.00 & 0 & 2500 \\\hline \text { Dela Mort } & 788.00 & 680.00 & 0 & 2000 \\\hline \text { Warax } & 800.00 & 700.00 & 100 & 1000 \\\hline \text { Invazen } & 850.00 & 800.00 & 80 & 500 \\\hline\\\hline \begin{array}{l}\text { Production rates } \\\text { units/hour) }\end{array} & \text { ScarCT } & \text { Dela Mort } & \text { Warax } & \text { Invazen } & \begin{array}{l}\text { Hours } \\\text { Available }\end{array} \\\hline \text { Assembly } & - & 35 & 25 & 20 & 220 \\\hline \text { Painting } & 35 & 20 & 15 & 10 & 220 \\\hline \text { Sound Testing } & 20 & 10 & 20 & 18 & 220 \\\hline \text { Inspection } & 10 & 12 & 8 & 5 & 220 \\\hline \text { Packaging } & 9 & 10 & 5 & 8 & 220\\\hline\end{array}$
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