Deck 13: Linear Optimization

Question 1

Use the following information to answer the following question(s), 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 works 5 hours per day. The finishing department has 5 workers, who also work a 5-hour shift. Each pair of Rockwell surfboards requires 3 labor hours in the fabrication department and 1.5 labor hours in finishing. The Limestone model requires 4.5 labor-hours in fabrication and 2 labor-hours in finishing. The company operates 6 days a week. It makes a per-unit profit of $60 on the Rockwell model and $75 on the Limestone model. Approximately 4.1 Rockwell models and 8.4 Limestone models are produced per day. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } && \\\hline 4 & & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Rockwell } & \text { Limestone } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 3 & 4.5 & 75 \\\hline 7 & \text { Finishing } & 1.5 & 2 & 25 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 60.00 & \$ 75.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Rockwell } & \text { Limestone } \\\hline 14 & \text { Quantity Produced } & 4.1 & 8.4 & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Limestone } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

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

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

Answer 1

50.10

Question 2

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

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

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

Answer 2

$ 391.30

Question 3

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

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

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

Answer 3

30.0

Question 4

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

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

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

Question 5

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

-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 6

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

-What is the total profit generated?

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

Question 7

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

-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

Question 8

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

-What is the Allowable Decrease for Graystone surfboards produced?

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

Question 9

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 10

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

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

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

Question 11

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 12

Use the following information to answer the following question(s), 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 works 5 hours per day. The finishing department has 5 workers, who also work a 5-hour shift. Each pair of Rockwell surfboards requires 3 labor hours in the fabrication department and 1.5 labor hours in finishing. The Limestone model requires 4.5 labor-hours in fabrication and 2 labor-hours in finishing. The company operates 6 days a week. It makes a per-unit profit of $60 on the Rockwell model and $75 on the Limestone model. Approximately 4.1 Rockwell models and 8.4 Limestone models are produced per day. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } && \\\hline 4 & & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Rockwell } & \text { Limestone } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 3 & 4.5 & 75 \\\hline 7 & \text { Finishing } & 1.5 & 2 & 25 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 60.00 & \$ 75.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Rockwell } & \text { Limestone } \\\hline 14 & \text { Quantity Produced } & 4.1 & 8.4 & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Limestone } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the total profit generated?

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

Question 13

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

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

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

Question 14

Use the following information to answer the following question(s), 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 works 5 hours per day. The finishing department has 5 workers, who also work a 5-hour shift. Each pair of Rockwell surfboards requires 3 labor hours in the fabrication department and 1.5 labor hours in finishing. The Limestone model requires 4.5 labor-hours in fabrication and 2 labor-hours in finishing. The company operates 6 days a week. It makes a per-unit profit of $60 on the Rockwell model and $75 on the Limestone model. Approximately 4.1 Rockwell models and 8.4 Limestone models are produced per day. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } && \\\hline 4 & & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Rockwell } & \text { Limestone } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 3 & 4.5 & 75 \\\hline 7 & \text { Finishing } & 1.5 & 2 & 25 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 60.00 & \$ 75.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Rockwell } & \text { Limestone } \\\hline 14 & \text { Quantity Produced } & 4.1 & 8.4 & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Limestone } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

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

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

Question 15

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

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

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

Question 16

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

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

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

Question 17

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

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

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

Question 18

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

-What is the Allowable Increase for Lava surfboards produced?

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

Question 19

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 20

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

-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 21

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

-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 22

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

-Which of the following approaches provided by the Analytic Solver Platform can automatically run multiple optimizations while varying model parameters within a predefined range?

A) sensitivity analysis
B) breakdown analysis
C) parameter analysis
D) uncertainty analysis

Question 23

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

-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 24

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

-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 25

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

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

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

Question 26

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

-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 27

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

-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 28

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

-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 29

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

-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 30

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

-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

Question 31

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

-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 32

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

-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 33

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

-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 34

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

-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 35

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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. $\begin{array}{|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & &&{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitation (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 & \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } \\\hline 14 & \text { QuantityProduced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & & & & \text { Total Profit } \\\hline 22 & \text { ProfitContribution } & & & \\\hline\end{array}$

-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 36

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

-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 37

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

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

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

Question 38

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

-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 39

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

-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 40

Use the following information to answer the question(s) 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. $\begin{array}{|l|l|l|l|l|l|l|}\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline& \text { Cerebro } && & & & \\1&\text { ManufacturingModel } & & & & & \\\hline 2\\\hline 3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips }& \begin{array}{l}\text { Machine } \\\text { Capacity } \\\text { (mins./year) }\end{array} \\\hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\\hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\\hline 6 & \text { Gross margin/minute } & \\\hline 7 & \text { Maximum production } & \\\hline 8 & \text { Profit } & \\\hline\end{array}$

-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 41

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

Question 42

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

Question 43

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

Question 44

What is the importance of Shadow Price in the Sensitivity Report?

Question 45

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

Question 46

Explain the simplex method used by Solver.

Question 47

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

Question 48

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

Question 49

What are the Excel functions to avoid in linear optimization?

Question 50

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