Deck 13: Linear Optimization

Question 1

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver.
Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. $\begin{array}{|l|c|c|c|c|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8\\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the total profit generated?

A) $ 675.68
B) $ 920.57
C) $ 521.74
D) $ 788.32

Answer 1

$ 521.74

Question 2

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver.
Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. $\begin{array}{|l|c|c|c|c|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8\\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the shadow price for the finishing hours used?

A) 32.46
B) 17.39
C) 8.33
D) 6.67

Answer 2

17.39

Question 3

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver.
Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. $\begin{array}{|l|c|c|c|c|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8\\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the Allowable Decrease for Graystone surfboards produced?

A) 30.74
B) 80.00
C) 12.33
D) 6.67

Answer 3

6.67

Question 4

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver.
Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. $\begin{array}{|l|c|c|c|c|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8\\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the Allowable Decrease in the fabrication hours used?

A) 26.84
B) 16.67
C) 8.33
D) 38.46

Question 5

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver.
Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. $\begin{array}{|l|c|c|c|c|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8\\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What will be the total profit contribution from Graystone surfboards?

A) $ 391.30
B) $ 521.74
C) $ 130.43
D) $ 276.65

Question 6

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver.
Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. $\begin{array}{|l|c|c|c|c|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8\\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the Allowable Increase for Lava surfboards produced?

A) 30
B) 24
C) 12
D) 18

Question 7

Use the following information to answer the questions) below.
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\\hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\\hline 2 & & \\\hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\\text { Capacity } \\\text { mins./year) } \\\end{array}\\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & & & & & \\\hline 7 & \text { Maximum production } & & & & & \\\hline 8 & \text { Profit } & & & & & \\\hline\end{array}$

-What is the gross margin per minute of rivets manufactured?

A) $ 0.60
B) $ 0.73
C) $ 0.40
D) $ 0.27

Question 8

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver.
Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. $\begin{array}{|l|c|c|c|c|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8\\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the total number of hours used for fabrication?

A) 54.5
B) 30.0
C) 35.5
D) 43.8

Question 9

Use the following information to answer the following questions), using the SUMPRODUCT function.
Stone Age Surfboards is a small manufacturer of two types of popular high-tide surfboards, the Rockwell and the Limestone models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 15 skilled workers, each of whom
What is the total profit generated?

A) $ 876.00
B) $ 675.50
C) $ 480.50
D) $ 965.00

Question 10

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver.
Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. $\begin{array}{|l|c|c|c|c|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8\\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the total number of hours used for the finishing operation?

A) 18.7
B) 30.0
C) 35.5
D) 24.2

Question 11

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver.
Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. $\begin{array}{|l|c|c|c|c|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8\\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the Allowable Increase in the finishing hours used?

A) 32.46
B) 8.33
C) 26.84
D) 16.67

Question 12

Use the following information to answer the questions) below.
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\\hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\\hline 2 & & \\\hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\\text { Capacity } \\\text { mins./year) } \\\end{array}\\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & & & & & \\\hline 7 & \text { Maximum production } & & & & & \\\hline 8 & \text { Profit } & & & & & \\\hline\end{array}$

-What is the gross margin per minute of plugs manufactured?

A) $ 0.60
B) $ 0.73
C) $ 0.40
D) $ 0.27

Question 13

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver.
Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. $\begin{array}{|l|c|c|c|c|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8\\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the value of slack obtained from the answer report?

A) 46.78
B) 38.46
C) 59.24
D) 23.85

Question 14

Use the following information to answer the following questions), using the SUMPRODUCT function.
Stone Age Surfboards is a small manufacturer of two types of popular high-tide surfboards, the Rockwell and the Limestone models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 15 skilled workers, each of whom
What is the total number of hours used for fabrication?

A) 42.58
B) 50.10
C) 35.64
D) 22.95

Question 15

Which of the following best defines objective functions?

A) They are limitations, requirements, or other restrictions that are imposed on any solution in an optimization model.
B) They are quantities that an optimization model seeks to maximize or minimize.
C) They are quantities for which no feasible solutions exist in an optimization model.
D) They are unknown values that an optimization model seeks to determine.

Question 16

Use the following information to answer the following questions), using the SUMPRODUCT function.
Stone Age Surfboards is a small manufacturer of two types of popular high-tide surfboards, the Rockwell and the Limestone models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 15 skilled workers, each of whom
What is the total number of hours used for the finishing operation?

A) 42.58
B) 50.10
C) 35.64
D) 22.95

Question 17

Which of the following best defines constraints in an optimization problem?

A) They are limitations, requirements, or other restrictions that are imposed on any solution.
B) They are quantities that an optimization model seeks to maximize or minimize.
C) They are quantities for which no feasible solutions exist.
D) They are unknown values that the model seeks to determine.

Question 18

Which of the following best defines decision variables in an optimization model?

A) They are limitations, requirements, or other restrictions that are imposed on any solution.
B) They are the quantities that the model seeks to maximize or minimize.
C) They are quantities for which no feasible solutions exist.
D) They are unknown values that the model seeks to determine.

Question 19

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver.
Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. $\begin{array}{|l|c|c|c|c|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8\\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What will be the total profit contribution from Lava surfboards?

A) $ 391.30
B) $ 521.74
C) $ 130.43
D) $ 276.65

Question 20

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver.
Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. $\begin{array}{|l|c|c|c|c|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8\\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-Which of the following solving methods is selected in the Solver dialog for linear and linear integer optimization problems?

A) GRG Nonlinear
B) Simplex LP
C) SOCP Barrier Engine
D) Evolutionary

Question 21

What are the two basic properties of a linear optimization model?

Question 22

Use the following information to answer the questions) below.
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\\hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\\hline 2 & & \\\hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\\text { Capacity } \\\text { mins./year) } \\\end{array}\\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & & & & & \\\hline 7 & \text { Maximum production } & & & & & \\\hline 8 & \text { Profit } & & & & & \\\hline\end{array}$

-When a model has a unique optimal solution, it means that .

A) the objective is maximized or minimized by more than one combination of decision variables
B) there is no solution that simultaneously satisfies all the constraints
C) the Allowable Increase or Allowable Decrease values for changing cells are zero
D) there is exactly one solution that will result in the maximum or minimum objective

Question 23

Any solution that satisfies all constraints of a problem is called a feasible solution.

Question 24

What are the four possible outcomes that can be obtained by solving a linear optimization model?

Question 25

Use the following information to answer the questions) below.
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\\hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\\hline 2 & & \\\hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\\text { Capacity } \\\text { mins./year) } \\\end{array}\\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & & & & & \\\hline 7 & \text { Maximum production } & & & & & \\\hline 8 & \text { Profit } & & & & & \\\hline\end{array}$

-What is the maximum possible production of rails based on the machine capacity?

A) 250,000.00
B) 83,333.33
C) 166,666.67
D) 125,000.00

Question 26

A constraint function is a function of the decision variables in the problem.

Question 27

Use the following information to answer the questions) below.
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\\hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\\hline 2 & & \\\hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\\text { Capacity } \\\text { mins./year) } \\\end{array}\\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & & & & & \\\hline 7 & \text { Maximum production } & & & & & \\\hline 8 & \text { Profit } & & & & & \\\hline\end{array}$

-What is the total profit generated from the manufacture of only plugs?

A) $ 66,666.67
B) $ 100,000.00
C) $ 183,333.33
D) $ 150,000.00

Question 28

Use the following information to answer the questions) below.
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\\hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\\hline 2 & & \\\hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\\text { Capacity } \\\text { mins./year) } \\\end{array}\\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & & & & & \\\hline 7 & \text { Maximum production } & & & & & \\\hline 8 & \text { Profit } & & & & & \\\hline\end{array}$

-What is the maximum production of clips based on the machine capacity?

A) 250,000.00
B) 83,333.33
C) 166,666.67
D) 125,000.00

Question 29

Explain the simplex method used by Solver.

Question 30

Use the following information to answer the questions) below.
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\\hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\\hline 2 & & \\\hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\\text { Capacity } \\\text { mins./year) } \\\end{array}\\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & & & & & \\\hline 7 & \text { Maximum production } & & & & & \\\hline 8 & \text { Profit } & & & & & \\\hline\end{array}$

-Which of the following options is used if Solver gives an error message that linearity is not satisfied?

A) Ignore Integer Constraints
B) Show Iteration Results
C) Use Automatic Scaling
D) Use Multistart

Question 31

Use the following information to answer the questions) below.
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\\hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\\hline 2 & & \\\hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\\text { Capacity } \\\text { mins./year) } \\\end{array}\\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & & & & & \\\hline 7 & \text { Maximum production } & & & & & \\\hline 8 & \text { Profit } & & & & & \\\hline\end{array}$

-What is the total profit generated from the manufacture of rivets?

A) $ 66,666.67
B) $ 100,000.00
C) $ 183,333.33
D) $ 150,000.00

Question 32

Use the following information to answer the questions) below.
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\\hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\\hline 2 & & \\\hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\\text { Capacity } \\\text { mins./year) } \\\end{array}\\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & & & & & \\\hline 7 & \text { Maximum production } & & & & & \\\hline 8 & \text { Profit } & & & & & \\\hline\end{array}$

-An infeasible problem is one for which .

A) the objective is maximized or minimized by more than one combination of decision variables
B) there is no solution that simultaneously satisfies all the constraints
C) the objective can be increased or decreased to infinity or negative infinity
D) there is exactly one solution that will result in the maximum or minimum objective

Question 33

Infeasible problems can occur when the demand requirement is higher than the available capacity.

Question 34

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 35

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 36

A binding constraint is one for which the Cell Value is greater than the right-hand side of the value of the constraint.

Question 37

Use the following information to answer the questions) below.
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\\hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\\hline 2 & & \\\hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\\text { Capacity } \\\text { mins./year) } \\\end{array}\\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & & & & & \\\hline 7 & \text { Maximum production } & & & & & \\\hline 8 & \text { Profit } & & & & & \\\hline\end{array}$

-Alternate optimal solutions exist when the .

A) reduced cost is equal to the shadow price
B) ratio of the objective coefficient to the constraint coefficient is one
C) Allowable Increase values for changing cells are zero
D) final value of the changing cells is greater than that of the constraints

Question 38

What are the Excel functions to avoid in linear optimization?

Question 39

Use the following information to answer the questions) below.
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\\hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\\hline 2 & & \\\hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\\text { Capacity } \\\text { mins./year) } \\\end{array}\\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & & & & & \\\hline 7 & \text { Maximum production } & & & & & \\\hline 8 & \text { Profit } & & & & & \\\hline\end{array}$

-An unbounded problem is one for which .

A) the objective is maximized or minimized by more than one combination of decision variables
B) there is no solution that simultaneously satisfies all the constraints
C) the objective can be increased or decreased to infinity or negative infinity while the solution remains feasible
D) there is exactly one solution that will result in the maximum or minimum objective

Question 40

Use the following information to answer the questions) below.
Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\\hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\\hline 2 & & \\\hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\\text { Capacity } \\\text { mins./year) } \\\end{array}\\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & & & & & \\\hline 7 & \text { Maximum production } & & & & & \\\hline 8 & \text { Profit } & & & & & \\\hline\end{array}$

-If a model has alternative optimal solutions, .

A) the objective is maximized or minimized by more than one combination of decision variables
B) there is no solution that simultaneously satisfies all the constraints
C) the objective can be increased or decreased to infinity or negative infinity
D) there is exactly one solution that will result in the maximum or minimum objective

Question 41

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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transpartation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) using a linear optimization model.

-Which of the following is the constraint for total amount shipped from Atlanta?

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

Question 42

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | } \hline \text { Datherin Hides } & & & \\\hline & & & \\\hline \text { Data }& & \\\hline & & & \\\hline & \text { Sumuner } & \text { Autumn } & \text { Winter } \\\hline \begin{array} { l } \text { Unit Production } \\\text { Cost }\end{array} & 12 & 13 & 15.5 \\\hline \text { Unit Inventory } & & & \\\text { Holding Cost } & 1.9 & 1.9 & 1.9 \\\hline \text { demand } & 200 & 450 & 500 \\\hline\end{array}$$ 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 43

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.

-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 44

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.

-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 45

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.

-Which of the following is the constraint for investment in low-priced and multinational funds?

A) X1 + X2 $\ge$ 0.35750,000)
B) $\frac { X _ { 1 } + X _ { 2 } } { 750,000 }$ $\ge$ 0.35750,000)
C) X1 + X2 + X3 + X4 + X5 + X6 $\ge$ 0.35750,000)
D) $\frac { X _ { 1 } + X _ { 2 } } { 750,000 }$ $\ge$ 0.35

Question 46

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. Answer the following questions) using a linear optimization model.
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 47

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 48

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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transpartation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) using a linear optimization model.

-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 $\le$ 0
B) Xij $\ge$ 0, for all i and j
C) Xij $\le$ 0, for all i and j
D) $\left( 13 X _ { 11 } + 15.25 X _ { 12 } + 10.99 X _ { 13 } + 18.48 X _ { 14 } - 10.75 X _ { 21 } + 15.16 X _ { 22 } + 9.65 X _ { 23 } + 18.5 X _ { 24 } \right) ( 1,250 / 750 ) \leq 0$

Question 49

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | } \hline \text { Datherin Hides } & & & \\\hline & & & \\\hline \text { Data }& & \\\hline & & & \\\hline & \text { Sumuner } & \text { Autumn } & \text { Winter } \\\hline \begin{array} { l } \text { Unit Production } \\\text { Cost }\end{array} & 12 & 13 & 15.5 \\\hline \text { Unit Inventory } & & & \\\text { Holding Cost } & 1.9 & 1.9 & 1.9 \\\hline \text { demand } & 200 & 450 & 500 \\\hline\end{array}$$ 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 50

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

Question 51

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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transpartation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) using a linear optimization model.

-Which of the following gives the constraint for the demand met at a distribution center?

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

Question 52

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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transpartation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) using a linear optimization model.

-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 53

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 54

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | } \hline \text { Datherin Hides } & & & \\\hline & & & \\\hline \text { Data }& & \\\hline & & & \\\hline & \text { Sumuner } & \text { Autumn } & \text { Winter } \\\hline \begin{array} { l } \text { Unit Production } \\\text { Cost }\end{array} & 12 & 13 & 15.5 \\\hline \text { Unit Inventory } & & & \\\text { Holding Cost } & 1.9 & 1.9 & 1.9 \\\hline \text { demand } & 200 & 450 & 500 \\\hline\end{array}$$ 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 55

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. Answer the following questions) using a linear optimization model.
List out the different types of constraints that help model formulation.

Question 56

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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transpartation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) using a linear optimization model.

-Which of the following is the constraint for total amount shipped from Dallas?

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

Question 57

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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transpartation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) using a linear optimization model.

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

Question 58

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. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Transpartation } & & & & & \\\text { Model } & & & & & \\\hline & & & & & \\\hline \text { Data } & & & & & \\\hline & \text { Distribution } & & & & \\& \text { Center } & & & & \\\hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\\hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\\hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\\hline \text { Dernand } & 175 & 325 & 480 & 950 & \\\hline\end{array}$$ Answer the following questions) using a linear optimization model.

-The mathematical form Y $\le$ 450 would be considered as representing a simple bounds constraint.

Question 59

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | } \hline \text { Datherin Hides } & & & \\\hline & & & \\\hline \text { Data }& & \\\hline & & & \\\hline & \text { Sumuner } & \text { Autumn } & \text { Winter } \\\hline \begin{array} { l } \text { Unit Production } \\\text { Cost }\end{array} & 12 & 13 & 15.5 \\\hline \text { Unit Inventory } & & & \\\text { Holding Cost } & 1.9 & 1.9 & 1.9 \\\hline \text { demand } & 200 & 450 & 500 \\\hline\end{array}$$ 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 60

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.

-Which of the following describes the constraint on the mid-cap fund?

A) X3 $\ge$ 0.35750,000)
B) X3 $\ge$ 80,000
C) X3 $\ge$ 0.3580,000)
D) X3 $\le$ 670,000

Question 61

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | } \hline \text { Datherin Hides } & & & \\\hline & & & \\\hline \text { Data }& & \\\hline & & & \\\hline & \text { Sumuner } & \text { Autumn } & \text { Winter } \\\hline \begin{array} { l } \text { Unit Production } \\\text { Cost }\end{array} & 12 & 13 & 15.5 \\\hline \text { Unit Inventory } & & & \\\text { Holding Cost } & 1.9 & 1.9 & 1.9 \\\hline \text { demand } & 200 & 450 & 500 \\\hline\end{array}$$ 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 62

Use the table below to answer the following questions).
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. $$\begin{array} { | l | l | l | l | } \hline \text { Datherin Hides } & & & \\\hline & & & \\\hline \text { Data }& & \\\hline & & & \\\hline & \text { Sumuner } & \text { Autumn } & \text { Winter } \\\hline \begin{array} { l } \text { Unit Production } \\\text { Cost }\end{array} & 12 & 13 & 15.5 \\\hline \text { Unit Inventory } & & & \\\text { Holding Cost } & 1.9 & 1.9 & 1.9 \\\hline \text { demand } & 200 & 450 & 500 \\\hline\end{array}$$ 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) $17,885
B) $15,605
C) $15,700
D) $18,700