Deck 15: Integer Optimization

Question 1

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver.
Coppell Services contracts with outsourcing partners to handle various customer service functions. Based on a study of call volumes provided by one of the firm's partners, the minimum number of staff needed for each hour of the day is as follows: $$\begin{array} { | l | l | } \hline \text { Hour } & \text { Minimum Staff Required } \\\hline 8 - 9 & 6 \\\hline 9 - 10 & 10 \\\hline 10 - 11 & 12 \\\hline 11 \text {-noon } & 10 \\\hline \text { noon-1 } & 8 \\\hline 1 - 2 & 16 \\\hline 2 - 3 & 15 \\\hline 3 - 4 & 20 \\\hline 4 - 5 & 15 \\\hline\end{array}$$ Mr. Coppell hires 6 permanent employees and wants to staff the remaining requirements using part-time employees who work 4-hour shifts (four consecutive hours starting as early as 8 A.M. or as late as 1 P.M.).

-How many excess employees are present in the noon-1 time slot?

A) 2
B) 4
C) 5
D) 6

Answer 1

5

Question 2

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 works9.25 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.
Use the spreadsheet below for Stone Age Surfboards to answer the following question(s) using integer constraints on variables in the optimization models using the standard Solver. $\begin{array}{|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitations (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } & \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & && & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the quantity of Lava surfboards produced?

A) 2
B) 5
C) 7
D) 10

Answer 2

7

Question 3

What should be the value of Integer Tolerance in order to find the guaranteed optimal integer solution?

A) -1
B) 0
C) 0.5
D) 1

Answer 3

B

Question 4

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 works9.25 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.
Use the spreadsheet below for Stone Age Surfboards to answer the following question(s) using integer constraints on variables in the optimization models using the standard Solver. $\begin{array}{|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitations (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } & \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & && & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

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

A) 39.6
B) 34.4
C) 29.2
D) 24.8

Question 5

Formulate and solve optimization models with binary variables and logical constraints.
Use the table below to answer the following question(s) by invoking the binary constraints on the variables using the standard Solver.
Below is the spreadsheet for a project selection model: $\begin{array}{|l|l|l|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\\hline & \text { Project Selection } & & & & & & \\1 & \text { Model } & & & & & & \\\hline 2 & & & & & & & \\\hline 3 & \text { Data } & & & & & & \\\hline 4 & & & & & & & \text { Available } \\ & & \text { Project 1 } & \text { Project 2 } & \text { Project 3 } & \text { Project 4 } & \text { Project 5 } & \text { Resources } \\\hline 5 & \begin{array}{l}\text { Expected Return } \\(\mathrm{NPV})\end{array} & \$ 160,000 & \$ 200,000 & \$ 125,000 & \$ 150,000 & \$ 225,000 \\\hline 6 & \begin{array}{l}\text { Cash } \\\text { requirements }\end{array} & \$ 45,000 & \$ 70,000 & \$ 28,000 & \$ 52,000 & \$ 65,000 &\$175,000\\\hline 7 & \begin{array}{l}\text { Personnel } \\\text { requirements }\end{array} & 7 & 4 & 2 & 6 & 4 & 10 \\\hline 8 & & & & & & & \\\hline 9 & \text { Model } \\\hline 10 & \\\hline 11 & \begin{array}{l}\text { Project selection } \\\text { decisions }\end{array} \\\hline 12 & \text { Cash Used } \\\hline 13 & \text { Personnel Used } \\\hline 14 & \text { Return } \\\hline\end{array}$

-What is the amount of cash used for Project 2?

A) $ 105,000
B) $ 25,000
C) $ 115,000
D) $ 70,000

Question 6

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 works9.25 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.
Use the spreadsheet below for Stone Age Surfboards to answer the following question(s) using integer constraints on variables in the optimization models using the standard Solver. $\begin{array}{|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitations (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } & \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & && & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the quantity of Graystone surfboards produced?

A) 2
B) 5
C) 7
D) 10

Question 7

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 works9.25 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.
Use the spreadsheet below for Stone Age Surfboards to answer the following question(s) using integer constraints on variables in the optimization models using the standard Solver. $\begin{array}{|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitations (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } & \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & && & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

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

A) 39.6
B) 34.4
C) 29.2
D) 24.8

Question 8

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver.
A company makes standard 130-inch-wide rolls of thin sheet metal and slits them into smaller rolls to meet customer orders for widths of 10, 14, and 25 inches. Suppose that the company has proposed the following cutting patterns: $\begin{array}{|c|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\\hline 1 & \text { Cutting-Stock Problem } & & & & \\\hline 2 & & & & & \\\hline 3 & \text { Data } & & & & \\\hline 4 & \text { Pattern } & \text { 10-in rolls } & \text { 14 in. rolls } & \text { 25-in. rolls } & \text { Scrap } \\\hline 5 & 1 & 0 & 8 & 0 & 10 \\\hline 6 & 2 & 0 & 2 & 3 & 10 \\\hline 7 & 3 & 3 & 0 & 3 & 4 \\\hline 8 & 4 & 10 & 0 & 0 & 10 \\\hline 9 & 5 & 3 & 2 & 2 & 4 \\\hline 10 & 6 & 8 & 2 & 0 & 4 \\\hline\end{array}$ Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls. Develop a model using the Analytic Solver Platform that will determine how many 130-inch rolls to cut into each of the six patterns in order to meet demand and minimize scrap.

-What is the total scrap produced?

A) 1,389
B) 1,390
C) 1,427
D) 1,445

Question 9

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver.
Coppell Services contracts with outsourcing partners to handle various customer service functions. Based on a study of call volumes provided by one of the firm's partners, the minimum number of staff needed for each hour of the day is as follows: $$\begin{array} { | l | l | } \hline \text { Hour } & \text { Minimum Staff Required } \\\hline 8 - 9 & 6 \\\hline 9 - 10 & 10 \\\hline 10 - 11 & 12 \\\hline 11 \text {-noon } & 10 \\\hline \text { noon-1 } & 8 \\\hline 1 - 2 & 16 \\\hline 2 - 3 & 15 \\\hline 3 - 4 & 20 \\\hline 4 - 5 & 15 \\\hline\end{array}$$ Mr. Coppell hires 6 permanent employees and wants to staff the remaining requirements using part-time employees who work 4-hour shifts (four consecutive hours starting as early as 8 A.M. or as late as 1 P.M.).

-How many excess employees are present in the 4-5 time slot?

A) 0
B) 2
C) 4
D) 6

Question 10

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 works9.25 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.
Use the spreadsheet below for Stone Age Surfboards to answer the following question(s) using integer constraints on variables in the optimization models using the standard Solver. $\begin{array}{|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitations (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } & \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & && & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-What is the total profit generated?

A) $ 748.28
B) $ 687.46
C) $ 385.65
D) $ 500.00

Question 11

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver.
Coppell Services contracts with outsourcing partners to handle various customer service functions. Based on a study of call volumes provided by one of the firm's partners, the minimum number of staff needed for each hour of the day is as follows: $$\begin{array} { | l | l | } \hline \text { Hour } & \text { Minimum Staff Required } \\\hline 8 - 9 & 6 \\\hline 9 - 10 & 10 \\\hline 10 - 11 & 12 \\\hline 11 \text {-noon } & 10 \\\hline \text { noon-1 } & 8 \\\hline 1 - 2 & 16 \\\hline 2 - 3 & 15 \\\hline 3 - 4 & 20 \\\hline 4 - 5 & 15 \\\hline\end{array}$$ Mr. Coppell hires 6 permanent employees and wants to staff the remaining requirements using part-time employees who work 4-hour shifts (four consecutive hours starting as early as 8 A.M. or as late as 1 P.M.).

-What is the minimum number of total part-time employees needed across all the 4-hour shifts to ensure meeting the staffing requirements?

A) 16
B) 28
C) 24
D) 20

Question 12

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver.
Coppell Services contracts with outsourcing partners to handle various customer service functions. Based on a study of call volumes provided by one of the firm's partners, the minimum number of staff needed for each hour of the day is as follows: $$\begin{array} { | l | l | } \hline \text { Hour } & \text { Minimum Staff Required } \\\hline 8 - 9 & 6 \\\hline 9 - 10 & 10 \\\hline 10 - 11 & 12 \\\hline 11 \text {-noon } & 10 \\\hline \text { noon-1 } & 8 \\\hline 1 - 2 & 16 \\\hline 2 - 3 & 15 \\\hline 3 - 4 & 20 \\\hline 4 - 5 & 15 \\\hline\end{array}$$ Mr. Coppell hires 6 permanent employees and wants to staff the remaining requirements using part-time employees who work 4-hour shifts (four consecutive hours starting as early as 8 A.M. or as late as 1 P.M.).

-How many part-time employees are present in the 3-4 time slot?

A) 16
B) 14
C) 9
D) 7

Question 13

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver.
Coppell Services contracts with outsourcing partners to handle various customer service functions. Based on a study of call volumes provided by one of the firm's partners, the minimum number of staff needed for each hour of the day is as follows: $$\begin{array} { | l | l | } \hline \text { Hour } & \text { Minimum Staff Required } \\\hline 8 - 9 & 6 \\\hline 9 - 10 & 10 \\\hline 10 - 11 & 12 \\\hline 11 \text {-noon } & 10 \\\hline \text { noon-1 } & 8 \\\hline 1 - 2 & 16 \\\hline 2 - 3 & 15 \\\hline 3 - 4 & 20 \\\hline 4 - 5 & 15 \\\hline\end{array}$$ Mr. Coppell hires 6 permanent employees and wants to staff the remaining requirements using part-time employees who work 4-hour shifts (four consecutive hours starting as early as 8 A.M. or as late as 1 P.M.).

-How many part-time employees are present in the 8-9 time slot?

A) 4
B) 6
C) 9
D) 14

Question 14

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver.
Coppell Services contracts with outsourcing partners to handle various customer service functions. Based on a study of call volumes provided by one of the firm's partners, the minimum number of staff needed for each hour of the day is as follows: $$\begin{array} { | l | l | } \hline \text { Hour } & \text { Minimum Staff Required } \\\hline 8 - 9 & 6 \\\hline 9 - 10 & 10 \\\hline 10 - 11 & 12 \\\hline 11 \text {-noon } & 10 \\\hline \text { noon-1 } & 8 \\\hline 1 - 2 & 16 \\\hline 2 - 3 & 15 \\\hline 3 - 4 & 20 \\\hline 4 - 5 & 15 \\\hline\end{array}$$ Mr. Coppell hires 6 permanent employees and wants to staff the remaining requirements using part-time employees who work 4-hour shifts (four consecutive hours starting as early as 8 A.M. or as late as 1 P.M.).

-Which of the following best defines a binary variable?

A) It is a general integer variable that is restricted to being between -1 and 1.
B) It is a general integer variable that is restricted to being a multiple of 2.
C) It is a general integer variable that is restricted to being between 0 and 1.
D) It is a general integer variable that is restricted to being greater than 2.

Question 15

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver.
A company makes standard 130-inch-wide rolls of thin sheet metal and slits them into smaller rolls to meet customer orders for widths of 10, 14, and 25 inches. Suppose that the company has proposed the following cutting patterns: $\begin{array}{|c|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\\hline 1 & \text { Cutting-Stock Problem } & & & & \\\hline 2 & & & & & \\\hline 3 & \text { Data } & & & & \\\hline 4 & \text { Pattern } & \text { 10-in rolls } & \text { 14 in. rolls } & \text { 25-in. rolls } & \text { Scrap } \\\hline 5 & 1 & 0 & 8 & 0 & 10 \\\hline 6 & 2 & 0 & 2 & 3 & 10 \\\hline 7 & 3 & 3 & 0 & 3 & 4 \\\hline 8 & 4 & 10 & 0 & 0 & 10 \\\hline 9 & 5 & 3 & 2 & 2 & 4 \\\hline 10 & 6 & 8 & 2 & 0 & 4 \\\hline\end{array}$ Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls. Develop a model using the Analytic Solver Platform that will determine how many 130-inch rolls to cut into each of the six patterns in order to meet demand and minimize scrap.

-What is the total number of 14-inch rolls produced?

A) 721
B) 725
C) 728
D) 740

Question 16

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver.
A company makes standard 130-inch-wide rolls of thin sheet metal and slits them into smaller rolls to meet customer orders for widths of 10, 14, and 25 inches. Suppose that the company has proposed the following cutting patterns: $\begin{array}{|c|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\\hline 1 & \text { Cutting-Stock Problem } & & & & \\\hline 2 & & & & & \\\hline 3 & \text { Data } & & & & \\\hline 4 & \text { Pattern } & \text { 10-in rolls } & \text { 14 in. rolls } & \text { 25-in. rolls } & \text { Scrap } \\\hline 5 & 1 & 0 & 8 & 0 & 10 \\\hline 6 & 2 & 0 & 2 & 3 & 10 \\\hline 7 & 3 & 3 & 0 & 3 & 4 \\\hline 8 & 4 & 10 & 0 & 0 & 10 \\\hline 9 & 5 & 3 & 2 & 2 & 4 \\\hline 10 & 6 & 8 & 2 & 0 & 4 \\\hline\end{array}$ Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls. Develop a model using the Analytic Solver Platform that will determine how many 130-inch rolls to cut into each of the six patterns in order to meet demand and minimize scrap.

-What is the total number of 10-inch rolls produced?

A) 940
B) 946
C) 950
D) 960

Question 17

is the parameter that specifies when the Solver algorithm will terminate an optimization process with integer constraints.

A) Mutation Rate
B) Population Size
C) Integer Tolerance
D) Convergence

Question 18

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver.
A company makes standard 130-inch-wide rolls of thin sheet metal and slits them into smaller rolls to meet customer orders for widths of 10, 14, and 25 inches. Suppose that the company has proposed the following cutting patterns: $\begin{array}{|c|c|c|c|c|c|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\\hline 1 & \text { Cutting-Stock Problem } & & & & \\\hline 2 & & & & & \\\hline 3 & \text { Data } & & & & \\\hline 4 & \text { Pattern } & \text { 10-in rolls } & \text { 14 in. rolls } & \text { 25-in. rolls } & \text { Scrap } \\\hline 5 & 1 & 0 & 8 & 0 & 10 \\\hline 6 & 2 & 0 & 2 & 3 & 10 \\\hline 7 & 3 & 3 & 0 & 3 & 4 \\\hline 8 & 4 & 10 & 0 & 0 & 10 \\\hline 9 & 5 & 3 & 2 & 2 & 4 \\\hline 10 & 6 & 8 & 2 & 0 & 4 \\\hline\end{array}$ Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls. Develop a model using the Analytic Solver Platform that will determine how many 130-inch rolls to cut into each of the six patterns in order to meet demand and minimize scrap.

-What is the total number of 25-inch rolls produced?

A) 630
B) 635
C) 640
D) 645

Question 19

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 works9.25 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.
Use the spreadsheet below for Stone Age Surfboards to answer the following question(s) using integer constraints on variables in the optimization models using the standard Solver. $\begin{array}{|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Stone Age Surfboards } & & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & & & \\\hline 4 & & &{\text { Product }} & \\\hline 5 & \text { Department } & \text { Graystone } & \text { Lava } & \text { Limitations (hours) } \\\hline 6 & \text { Fabrication } & 2.5 & 4.2 & 74 \\\hline 7 & \text { Finishing } & 2 & 3.6 & 30 \\\hline 8 & & & \\\hline 9 & \text { Profit/Unit } & \$ 40.00 & \$ 60.00 \\\hline 10 & & & \\\hline 11 & & & \\\hline 12 & \text { Model } & & \\\hline 13 & & \text { Graystone } & \text { Lava } & \\\hline 14 & \text { Quantity Produced } & & & \text { Hours Used } \\\hline 15 & \text { Fabrication } & & & \\\hline 16 & \text { Finishing } & & & \\\hline 17 & & & & \\\hline 18 & & & & \text { Excess Lava } \\\hline 19 & \text { Market Mixture } & & & \\\hline 20 & & & & \\\hline 21 & && & \text { Total Profit } \\\hline 22 & \text { Profit Contribution } & & & \\\hline\end{array}$

-Which of the following constraints Solver uses?

A) $B$14:$C$14 = integer
B) $D$15 > = $D$6
C) $D$16 > = $D$7
D) $D$19 < = 0

Question 20

Formulate and solve optimization models with binary variables and logical constraints.
Use the table below to answer the following question(s) by invoking the binary constraints on the variables using the standard Solver.
Below is the spreadsheet for a project selection model: $\begin{array}{|l|l|l|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\\hline & \text { Project Selection } & & & & & & \\1 & \text { Model } & & & & & & \\\hline 2 & & & & & & & \\\hline 3 & \text { Data } & & & & & & \\\hline 4 & & & & & & & \text { Available } \\ & & \text { Project 1 } & \text { Project 2 } & \text { Project 3 } & \text { Project 4 } & \text { Project 5 } & \text { Resources } \\\hline 5 & \begin{array}{l}\text { Expected Return } \\(\mathrm{NPV})\end{array} & \$ 160,000 & \$ 200,000 & \$ 125,000 & \$ 150,000 & \$ 225,000 \\\hline 6 & \begin{array}{l}\text { Cash } \\\text { requirements }\end{array} & \$ 45,000 & \$ 70,000 & \$ 28,000 & \$ 52,000 & \$ 65,000 &\$175,000\\\hline 7 & \begin{array}{l}\text { Personnel } \\\text { requirements }\end{array} & 7 & 4 & 2 & 6 & 4 & 10 \\\hline 8 & & & & & & & \\\hline 9 & \text { Model } \\\hline 10 & \\\hline 11 & \begin{array}{l}\text { Project selection } \\\text { decisions }\end{array} \\\hline 12 & \text { Cash Used } \\\hline 13 & \text { Personnel Used } \\\hline 14 & \text { Return } \\\hline\end{array}$

-Which of the following cells is set as the objective cell in Solver?

A) $G$12
B) $F$14
C) $G$14
D) $B$12

Question 21

Formulate and solve optimization models with binary variables and logical constraints. LO2: Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for a plant location model: $\begin{array}{|l|l|l|l|l|l|l|}\hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline 1 & \begin{array}{l}\text { Plant Location } \\\text { Model }\end{array} & & & & & \\\hline 2 & & & & & & \\\hline 3 & \text { Data } & & & & & \\\hline4&&&\text { Distribution Center }\\\hline 5 & \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jacksonville } & \text { Memphis } & \text { Capacity } \\\hline 6 & \text { Dallas } & \$ 11.80 & \$ 16.48 & \$ 12.35 & \$ 18.56 & 1,300 \\\hline 7 & \text { Atlanta } & \$ 8.54 & \$ 14.65 & \$ 9.58 & \$ 18.25 & 750 \\\hline 8 & \text { Detroit } & \$ 12.89 & \$ 10.78 & \$ 7.85 & \$ 10.28 & 1,400 \\\hline 9 & \text { Baltimore } & \$ 14.36 & \$ 18.95 & \$ 14.61 & \$ 6.64 & 1,300 \\\hline 10 & \text { Demand } & 350 & 450 & 800 & 1,700 & \\\hline 11 & \\\hline 12 & \text { Model } \\\hline 13 & \\\hline 14 & \text { Amount Shipped }&&\text { Distribution Center } \\\hline 15 & \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jack sonville } & \text { Memphis } & \text { Total Shipped } \\\hline 16 & \text { Dallas } & & & & & \\\hline 17 & \text { Atlanta } \\\hline 18 & \text { Detroit } \\\hline 19 & \text { Baltimore } \\\hline 20 & \text { Supply } \\\hline 21 & \\\hline 22 & \text { Total Cost } \\\hline 23 & \$ 0.00 \\\hline\end{array}$

-Which of the following constraints is used in Solver?

A) $F$16:$F$19 >= $F$6:$F$9
B) $B$20:$E$20 < $B$10:$E$10
C) $B$20:$E$20 = binary
D) $F$16:$F$19 <= $F$6:$F$9

Question 22

Formulate and solve optimization models with binary variables and logical constraints.
Use the table below to answer the following question(s) by invoking the binary constraints on the variables using the standard Solver.
Below is the spreadsheet for a project selection model: $\begin{array}{|l|l|l|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\\hline & \text { Project Selection } & & & & & & \\1 & \text { Model } & & & & & & \\\hline 2 & & & & & & & \\\hline 3 & \text { Data } & & & & & & \\\hline 4 & & & & & & & \text { Available } \\ & & \text { Project 1 } & \text { Project 2 } & \text { Project 3 } & \text { Project 4 } & \text { Project 5 } & \text { Resources } \\\hline 5 & \begin{array}{l}\text { Expected Return } \\(\mathrm{NPV})\end{array} & \$ 160,000 & \$ 200,000 & \$ 125,000 & \$ 150,000 & \$ 225,000 \\\hline 6 & \begin{array}{l}\text { Cash } \\\text { requirements }\end{array} & \$ 45,000 & \$ 70,000 & \$ 28,000 & \$ 52,000 & \$ 65,000 &\$175,000\\\hline 7 & \begin{array}{l}\text { Personnel } \\\text { requirements }\end{array} & 7 & 4 & 2 & 6 & 4 & 10 \\\hline 8 & & & & & & & \\\hline 9 & \text { Model } \\\hline 10 & \\\hline 11 & \begin{array}{l}\text { Project selection } \\\text { decisions }\end{array} \\\hline 12 & \text { Cash Used } \\\hline 13 & \text { Personnel Used } \\\hline 14 & \text { Return } \\\hline\end{array}$

-What is the amount of cash used for Project 5?

A) $ 65,000
B) $ 117,000
C) $ 13,000
D) $ 110,000

Question 23

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for Memphis Designs fixed cost model: $\begin{array}{|l|c|c|c|c|}\hline & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} \\\hline 1 &{\text { Memphis Design Fixed Cost Model }} & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & \\\hline 4 & & \\\hline 5 & \text { Cost } & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 6 & \text { Production } & \$ 10.00 & \$ 15.00 & \$ 13.50 \\\hline 7 & \text { Inventory } & \$ 1.70 & \$ 1.70 & \$ 1.70 \\\hline 8 & \text { Demand } & 200 & 450 & 75 \\\hline 9 & \text { Fixed Cost } & \$ 75.00 & \$ 75.00 & \$ 75.00 \\\hline 10 & \\\hline 11 & \text { Model } \\\hline 12 & \\\hline 13 & & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 14 & \text { Production } & & & \\\hline 15 & \text { Inventory } \\\hline 16 & \text { Binary } \\\hline 17 & \\\hline 18 & \text { Binary constraints } \\\hline 19 & \text { Net Production } \\\hline 20 & & \\\hline 21 & & \text { Cost } \\\hline 22 & \text { Total } & \\\hline\end{array}$

-What is the total cost incurred by the company?

A) $ 8,345.00
B) $ 10,756.80
C) $ 7,289.62
D) $ 9,582.75

Question 24

Formulate and solve optimization models with binary variables and logical constraints. LO2: Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for a plant location model: $\begin{array}{|l|l|l|l|l|l|l|}\hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline 1 & \begin{array}{l}\text { Plant Location } \\\text { Model }\end{array} & & & & & \\\hline 2 & & & & & & \\\hline 3 & \text { Data } & & & & & \\\hline4&&&\text { Distribution Center }\\\hline 5 & \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jacksonville } & \text { Memphis } & \text { Capacity } \\\hline 6 & \text { Dallas } & \$ 11.80 & \$ 16.48 & \$ 12.35 & \$ 18.56 & 1,300 \\\hline 7 & \text { Atlanta } & \$ 8.54 & \$ 14.65 & \$ 9.58 & \$ 18.25 & 750 \\\hline 8 & \text { Detroit } & \$ 12.89 & \$ 10.78 & \$ 7.85 & \$ 10.28 & 1,400 \\\hline 9 & \text { Baltimore } & \$ 14.36 & \$ 18.95 & \$ 14.61 & \$ 6.64 & 1,300 \\\hline 10 & \text { Demand } & 350 & 450 & 800 & 1,700 & \\\hline 11 & \\\hline 12 & \text { Model } \\\hline 13 & \\\hline 14 & \text { Amount Shipped }&&\text { Distribution Center } \\\hline 15 & \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jack sonville } & \text { Memphis } & \text { Total Shipped } \\\hline 16 & \text { Dallas } & & & & & \\\hline 17 & \text { Atlanta } \\\hline 18 & \text { Detroit } \\\hline 19 & \text { Baltimore } \\\hline 20 & \text { Supply } \\\hline 21 & \\\hline 22 & \text { Total Cost } \\\hline 23 & \$ 0.00 \\\hline\end{array}$

-What is the total cost incurred?

A) $ 27,297
B) $ 35,233
C) $ 42,675
D) $ 47,864

Question 25

Formulate and solve optimization models with binary variables and logical constraints. LO2: Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for a plant location model: $\begin{array}{|l|l|l|l|l|l|l|}\hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline 1 & \begin{array}{l}\text { Plant Location } \\\text { Model }\end{array} & & & & & \\\hline 2 & & & & & & \\\hline 3 & \text { Data } & & & & & \\\hline4&&&\text { Distribution Center }\\\hline 5 & \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jacksonville } & \text { Memphis } & \text { Capacity } \\\hline 6 & \text { Dallas } & \$ 11.80 & \$ 16.48 & \$ 12.35 & \$ 18.56 & 1,300 \\\hline 7 & \text { Atlanta } & \$ 8.54 & \$ 14.65 & \$ 9.58 & \$ 18.25 & 750 \\\hline 8 & \text { Detroit } & \$ 12.89 & \$ 10.78 & \$ 7.85 & \$ 10.28 & 1,400 \\\hline 9 & \text { Baltimore } & \$ 14.36 & \$ 18.95 & \$ 14.61 & \$ 6.64 & 1,300 \\\hline 10 & \text { Demand } & 350 & 450 & 800 & 1,700 & \\\hline 11 & \\\hline 12 & \text { Model } \\\hline 13 & \\\hline 14 & \text { Amount Shipped }&&\text { Distribution Center } \\\hline 15 & \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jack sonville } & \text { Memphis } & \text { Total Shipped } \\\hline 16 & \text { Dallas } & & & & & \\\hline 17 & \text { Atlanta } \\\hline 18 & \text { Detroit } \\\hline 19 & \text { Baltimore } \\\hline 20 & \text { Supply } \\\hline 21 & \\\hline 22 & \text { Total Cost } \\\hline 23 & \$ 0.00 \\\hline\end{array}$

-What is the total amount shipped by the Detroit plant to the distribution centers?

A) 750
B) 1,000
C) 1,400
D) 1,300

Question 26

Formulate and solve optimization models with binary variables and logical constraints. LO2: Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for a plant location model: $\begin{array}{|l|l|l|l|l|l|l|}\hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline 1 & \begin{array}{l}\text { Plant Location } \\\text { Model }\end{array} & & & & & \\\hline 2 & & & & & & \\\hline 3 & \text { Data } & & & & & \\\hline4&&&\text { Distribution Center }\\\hline 5 & \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jacksonville } & \text { Memphis } & \text { Capacity } \\\hline 6 & \text { Dallas } & \$ 11.80 & \$ 16.48 & \$ 12.35 & \$ 18.56 & 1,300 \\\hline 7 & \text { Atlanta } & \$ 8.54 & \$ 14.65 & \$ 9.58 & \$ 18.25 & 750 \\\hline 8 & \text { Detroit } & \$ 12.89 & \$ 10.78 & \$ 7.85 & \$ 10.28 & 1,400 \\\hline 9 & \text { Baltimore } & \$ 14.36 & \$ 18.95 & \$ 14.61 & \$ 6.64 & 1,300 \\\hline 10 & \text { Demand } & 350 & 450 & 800 & 1,700 & \\\hline 11 & \\\hline 12 & \text { Model } \\\hline 13 & \\\hline 14 & \text { Amount Shipped }&&\text { Distribution Center } \\\hline 15 & \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jack sonville } & \text { Memphis } & \text { Total Shipped } \\\hline 16 & \text { Dallas } & & & & & \\\hline 17 & \text { Atlanta } \\\hline 18 & \text { Detroit } \\\hline 19 & \text { Baltimore } \\\hline 20 & \text { Supply } \\\hline 21 & \\\hline 22 & \text { Total Cost } \\\hline 23 & \$ 0.00 \\\hline\end{array}$

-What is the total amount shipped by the Atlanta plant to the distribution centers?

A) 600
B) 1,000
C) 1,250
D) 1,300

Question 27

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for Memphis Designs fixed cost model: $\begin{array}{|l|c|c|c|c|}\hline & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} \\\hline 1 &{\text { Memphis Design Fixed Cost Model }} & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & \\\hline 4 & & \\\hline 5 & \text { Cost } & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 6 & \text { Production } & \$ 10.00 & \$ 15.00 & \$ 13.50 \\\hline 7 & \text { Inventory } & \$ 1.70 & \$ 1.70 & \$ 1.70 \\\hline 8 & \text { Demand } & 200 & 450 & 75 \\\hline 9 & \text { Fixed Cost } & \$ 75.00 & \$ 75.00 & \$ 75.00 \\\hline 10 & \\\hline 11 & \text { Model } \\\hline 12 & \\\hline 13 & & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 14 & \text { Production } & & & \\\hline 15 & \text { Inventory } \\\hline 16 & \text { Binary } \\\hline 17 & \\\hline 18 & \text { Binary constraints } \\\hline 19 & \text { Net Production } \\\hline 20 & & \\\hline 21 & & \text { Cost } \\\hline 22 & \text { Total } & \\\hline\end{array}$

-What is the net production at the end of the second quarter?

A) 75
B) 200
C) 450
D) 600

Question 28

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for Memphis Designs fixed cost model: $\begin{array}{|l|c|c|c|c|}\hline & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} \\\hline 1 &{\text { Memphis Design Fixed Cost Model }} & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & \\\hline 4 & & \\\hline 5 & \text { Cost } & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 6 & \text { Production } & \$ 10.00 & \$ 15.00 & \$ 13.50 \\\hline 7 & \text { Inventory } & \$ 1.70 & \$ 1.70 & \$ 1.70 \\\hline 8 & \text { Demand } & 200 & 450 & 75 \\\hline 9 & \text { Fixed Cost } & \$ 75.00 & \$ 75.00 & \$ 75.00 \\\hline 10 & \\\hline 11 & \text { Model } \\\hline 12 & \\\hline 13 & & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 14 & \text { Production } & & & \\\hline 15 & \text { Inventory } \\\hline 16 & \text { Binary } \\\hline 17 & \\\hline 18 & \text { Binary constraints } \\\hline 19 & \text { Net Production } \\\hline 20 & & \\\hline 21 & & \text { Cost } \\\hline 22 & \text { Total } & \\\hline\end{array}$

-What is the net production at the end of the third quarter?

A) 75
B) 200
C) 450
D) 600

Question 29

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for Memphis Designs fixed cost model: $\begin{array}{|l|c|c|c|c|}\hline & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} \\\hline 1 &{\text { Memphis Design Fixed Cost Model }} & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & \\\hline 4 & & \\\hline 5 & \text { Cost } & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 6 & \text { Production } & \$ 10.00 & \$ 15.00 & \$ 13.50 \\\hline 7 & \text { Inventory } & \$ 1.70 & \$ 1.70 & \$ 1.70 \\\hline 8 & \text { Demand } & 200 & 450 & 75 \\\hline 9 & \text { Fixed Cost } & \$ 75.00 & \$ 75.00 & \$ 75.00 \\\hline 10 & \\\hline 11 & \text { Model } \\\hline 12 & \\\hline 13 & & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 14 & \text { Production } & & & \\\hline 15 & \text { Inventory } \\\hline 16 & \text { Binary } \\\hline 17 & \\\hline 18 & \text { Binary constraints } \\\hline 19 & \text { Net Production } \\\hline 20 & & \\\hline 21 & & \text { Cost } \\\hline 22 & \text { Total } & \\\hline\end{array}$

-What is the net production at the end of the first quarter?

A) 75
B) 200
C) 450
D) 600

Question 30

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for Memphis Designs fixed cost model: $\begin{array}{|l|c|c|c|c|}\hline & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} \\\hline 1 &{\text { Memphis Design Fixed Cost Model }} & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & \\\hline 4 & & \\\hline 5 & \text { Cost } & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 6 & \text { Production } & \$ 10.00 & \$ 15.00 & \$ 13.50 \\\hline 7 & \text { Inventory } & \$ 1.70 & \$ 1.70 & \$ 1.70 \\\hline 8 & \text { Demand } & 200 & 450 & 75 \\\hline 9 & \text { Fixed Cost } & \$ 75.00 & \$ 75.00 & \$ 75.00 \\\hline 10 & \\\hline 11 & \text { Model } \\\hline 12 & \\\hline 13 & & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 14 & \text { Production } & & & \\\hline 15 & \text { Inventory } \\\hline 16 & \text { Binary } \\\hline 17 & \\\hline 18 & \text { Binary constraints } \\\hline 19 & \text { Net Production } \\\hline 20 & & \\\hline 21 & & \text { Cost } \\\hline 22 & \text { Total } & \\\hline\end{array}$

-What is the inventory at the end of the first quarter?

A) 725
B) 525
C) 50
D) 75

Question 31

Formulate and solve optimization models with binary variables and logical constraints. LO2: Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for a plant location model: $\begin{array}{|l|l|l|l|l|l|l|}\hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline 1 & \begin{array}{l}\text { Plant Location } \\\text { Model }\end{array} & & & & & \\\hline 2 & & & & & & \\\hline 3 & \text { Data } & & & & & \\\hline4&&&\text { Distribution Center }\\\hline 5 & \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jacksonville } & \text { Memphis } & \text { Capacity } \\\hline 6 & \text { Dallas } & \$ 11.80 & \$ 16.48 & \$ 12.35 & \$ 18.56 & 1,300 \\\hline 7 & \text { Atlanta } & \$ 8.54 & \$ 14.65 & \$ 9.58 & \$ 18.25 & 750 \\\hline 8 & \text { Detroit } & \$ 12.89 & \$ 10.78 & \$ 7.85 & \$ 10.28 & 1,400 \\\hline 9 & \text { Baltimore } & \$ 14.36 & \$ 18.95 & \$ 14.61 & \$ 6.64 & 1,300 \\\hline 10 & \text { Demand } & 350 & 450 & 800 & 1,700 & \\\hline 11 & \\\hline 12 & \text { Model } \\\hline 13 & \\\hline 14 & \text { Amount Shipped }&&\text { Distribution Center } \\\hline 15 & \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jack sonville } & \text { Memphis } & \text { Total Shipped } \\\hline 16 & \text { Dallas } & & & & & \\\hline 17 & \text { Atlanta } \\\hline 18 & \text { Detroit } \\\hline 19 & \text { Baltimore } \\\hline 20 & \text { Supply } \\\hline 21 & \\\hline 22 & \text { Total Cost } \\\hline 23 & \$ 0.00 \\\hline\end{array}$

-In which of the following plants is the total amount shipped to the distribution centers equal to zero?

A) Dallas
B) Atlanta
C) Detroit
D) Baltimore

Question 32

Formulate and solve optimization models with binary variables and logical constraints.
Use the table below to answer the following question(s) by invoking the binary constraints on the variables using the standard Solver.
Below is the spreadsheet for a project selection model: $\begin{array}{|l|l|l|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\\hline & \text { Project Selection } & & & & & & \\1 & \text { Model } & & & & & & \\\hline 2 & & & & & & & \\\hline 3 & \text { Data } & & & & & & \\\hline 4 & & & & & & & \text { Available } \\ & & \text { Project 1 } & \text { Project 2 } & \text { Project 3 } & \text { Project 4 } & \text { Project 5 } & \text { Resources } \\\hline 5 & \begin{array}{l}\text { Expected Return } \\(\mathrm{NPV})\end{array} & \$ 160,000 & \$ 200,000 & \$ 125,000 & \$ 150,000 & \$ 225,000 \\\hline 6 & \begin{array}{l}\text { Cash } \\\text { requirements }\end{array} & \$ 45,000 & \$ 70,000 & \$ 28,000 & \$ 52,000 & \$ 65,000 &\$175,000\\\hline 7 & \begin{array}{l}\text { Personnel } \\\text { requirements }\end{array} & 7 & 4 & 2 & 6 & 4 & 10 \\\hline 8 & & & & & & & \\\hline 9 & \text { Model } \\\hline 10 & \\\hline 11 & \begin{array}{l}\text { Project selection } \\\text { decisions }\end{array} \\\hline 12 & \text { Cash Used } \\\hline 13 & \text { Personnel Used } \\\hline 14 & \text { Return } \\\hline\end{array}$

-What is the amount of personnel used for Project 2?

A) 3
B) 4
C) 6
D) 11

Question 33

Formulate and solve optimization models with binary variables and logical constraints. LO2: Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for a plant location model: $\begin{array}{|l|l|l|l|l|l|l|}\hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline 1 & \begin{array}{l}\text { Plant Location } \\\text { Model }\end{array} & & & & & \\\hline 2 & & & & & & \\\hline 3 & \text { Data } & & & & & \\\hline4&&&\text { Distribution Center }\\\hline 5 & \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jacksonville } & \text { Memphis } & \text { Capacity } \\\hline 6 & \text { Dallas } & \$ 11.80 & \$ 16.48 & \$ 12.35 & \$ 18.56 & 1,300 \\\hline 7 & \text { Atlanta } & \$ 8.54 & \$ 14.65 & \$ 9.58 & \$ 18.25 & 750 \\\hline 8 & \text { Detroit } & \$ 12.89 & \$ 10.78 & \$ 7.85 & \$ 10.28 & 1,400 \\\hline 9 & \text { Baltimore } & \$ 14.36 & \$ 18.95 & \$ 14.61 & \$ 6.64 & 1,300 \\\hline 10 & \text { Demand } & 350 & 450 & 800 & 1,700 & \\\hline 11 & \\\hline 12 & \text { Model } \\\hline 13 & \\\hline 14 & \text { Amount Shipped }&&\text { Distribution Center } \\\hline 15 & \text { Plant } & \text { Houston } & \text { San Jose } & \text { Jack sonville } & \text { Memphis } & \text { Total Shipped } \\\hline 16 & \text { Dallas } & & & & & \\\hline 17 & \text { Atlanta } \\\hline 18 & \text { Detroit } \\\hline 19 & \text { Baltimore } \\\hline 20 & \text { Supply } \\\hline 21 & \\\hline 22 & \text { Total Cost } \\\hline 23 & \$ 0.00 \\\hline\end{array}$

-What is the total amount shipped by the Baltimore plant to the distribution centers?

A) 750
B) 1,000
C) 1,250
D) 1,300

Question 34

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for Memphis Designs fixed cost model: $\begin{array}{|l|c|c|c|c|}\hline & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} \\\hline 1 &{\text { Memphis Design Fixed Cost Model }} & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & \\\hline 4 & & \\\hline 5 & \text { Cost } & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 6 & \text { Production } & \$ 10.00 & \$ 15.00 & \$ 13.50 \\\hline 7 & \text { Inventory } & \$ 1.70 & \$ 1.70 & \$ 1.70 \\\hline 8 & \text { Demand } & 200 & 450 & 75 \\\hline 9 & \text { Fixed Cost } & \$ 75.00 & \$ 75.00 & \$ 75.00 \\\hline 10 & \\\hline 11 & \text { Model } \\\hline 12 & \\\hline 13 & & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 14 & \text { Production } & & & \\\hline 15 & \text { Inventory } \\\hline 16 & \text { Binary } \\\hline 17 & \\\hline 18 & \text { Binary constraints } \\\hline 19 & \text { Net Production } \\\hline 20 & & \\\hline 21 & & \text { Cost } \\\hline 22 & \text { Total } & \\\hline\end{array}$

-What is the binary constraint at the end of the third quarter?

A) 75
B) 200
C) 450
D) 0

Question 35

Formulate and solve optimization models with binary variables and logical constraints.
Use the table below to answer the following question(s) by invoking the binary constraints on the variables using the standard Solver.
Below is the spreadsheet for a project selection model: $\begin{array}{|l|l|l|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\\hline & \text { Project Selection } & & & & & & \\1 & \text { Model } & & & & & & \\\hline 2 & & & & & & & \\\hline 3 & \text { Data } & & & & & & \\\hline 4 & & & & & & & \text { Available } \\ & & \text { Project 1 } & \text { Project 2 } & \text { Project 3 } & \text { Project 4 } & \text { Project 5 } & \text { Resources } \\\hline 5 & \begin{array}{l}\text { Expected Return } \\(\mathrm{NPV})\end{array} & \$ 160,000 & \$ 200,000 & \$ 125,000 & \$ 150,000 & \$ 225,000 \\\hline 6 & \begin{array}{l}\text { Cash } \\\text { requirements }\end{array} & \$ 45,000 & \$ 70,000 & \$ 28,000 & \$ 52,000 & \$ 65,000 &\$175,000\\\hline 7 & \begin{array}{l}\text { Personnel } \\\text { requirements }\end{array} & 7 & 4 & 2 & 6 & 4 & 10 \\\hline 8 & & & & & & & \\\hline 9 & \text { Model } \\\hline 10 & \\\hline 11 & \begin{array}{l}\text { Project selection } \\\text { decisions }\end{array} \\\hline 12 & \text { Cash Used } \\\hline 13 & \text { Personnel Used } \\\hline 14 & \text { Return } \\\hline\end{array}$

-What is the total return obtained from all five projects?

A) $ 860,000
B) $ 550,000
C) $ 700,000
D) $ 395,000

Question 36

Formulate and solve optimization models with binary variables and logical constraints.
Use the table below to answer the following question(s) by invoking the binary constraints on the variables using the standard Solver.
Below is the spreadsheet for a project selection model: $\begin{array}{|l|l|l|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\\hline & \text { Project Selection } & & & & & & \\1 & \text { Model } & & & & & & \\\hline 2 & & & & & & & \\\hline 3 & \text { Data } & & & & & & \\\hline 4 & & & & & & & \text { Available } \\ & & \text { Project 1 } & \text { Project 2 } & \text { Project 3 } & \text { Project 4 } & \text { Project 5 } & \text { Resources } \\\hline 5 & \begin{array}{l}\text { Expected Return } \\(\mathrm{NPV})\end{array} & \$ 160,000 & \$ 200,000 & \$ 125,000 & \$ 150,000 & \$ 225,000 \\\hline 6 & \begin{array}{l}\text { Cash } \\\text { requirements }\end{array} & \$ 45,000 & \$ 70,000 & \$ 28,000 & \$ 52,000 & \$ 65,000 &\$175,000\\\hline 7 & \begin{array}{l}\text { Personnel } \\\text { requirements }\end{array} & 7 & 4 & 2 & 6 & 4 & 10 \\\hline 8 & & & & & & & \\\hline 9 & \text { Model } \\\hline 10 & \\\hline 11 & \begin{array}{l}\text { Project selection } \\\text { decisions }\end{array} \\\hline 12 & \text { Cash Used } \\\hline 13 & \text { Personnel Used } \\\hline 14 & \text { Return } \\\hline\end{array}$

-What is the return obtained from Project 3?

A) $ 200,000
B) $ 125,000
C) $ 275,000
D) $ 225,000

Question 37

Use a modern software tool to perform statistical calculations.
Use the table below to answer the following question(s) using the standard Solver. Below is the spreadsheet for Memphis Designs fixed cost model: $\begin{array}{|l|c|c|c|c|}\hline & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} \\\hline 1 &{\text { Memphis Design Fixed Cost Model }} & & \\\hline 2 & & & & \\\hline 3 & \text { Data } & \\\hline 4 & & \\\hline 5 & \text { Cost } & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 6 & \text { Production } & \$ 10.00 & \$ 15.00 & \$ 13.50 \\\hline 7 & \text { Inventory } & \$ 1.70 & \$ 1.70 & \$ 1.70 \\\hline 8 & \text { Demand } & 200 & 450 & 75 \\\hline 9 & \text { Fixed Cost } & \$ 75.00 & \$ 75.00 & \$ 75.00 \\\hline 10 & \\\hline 11 & \text { Model } \\\hline 12 & \\\hline 13 & & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } \\\hline 14 & \text { Production } & & & \\\hline 15 & \text { Inventory } \\\hline 16 & \text { Binary } \\\hline 17 & \\\hline 18 & \text { Binary constraints } \\\hline 19 & \text { Net Production } \\\hline 20 & & \\\hline 21 & & \text { Cost } \\\hline 22 & \text { Total } & \\\hline\end{array}$

-Which of the following constraints is used in Solver?

A) $B$14:$D$14 > = $B$18:$D$18
B) $B$16:$D$16 = binary
C) $B$19:$D$19 < = $B$8:$D$8
D) $B$15:$D$15 = binary

Question 38

Formulate and solve optimization models with binary variables and logical constraints.
Use the table below to answer the following question(s) by invoking the binary constraints on the variables using the standard Solver.
Below is the spreadsheet for a project selection model: $\begin{array}{|l|l|l|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\\hline & \text { Project Selection } & & & & & & \\1 & \text { Model } & & & & & & \\\hline 2 & & & & & & & \\\hline 3 & \text { Data } & & & & & & \\\hline 4 & & & & & & & \text { Available } \\ & & \text { Project 1 } & \text { Project 2 } & \text { Project 3 } & \text { Project 4 } & \text { Project 5 } & \text { Resources } \\\hline 5 & \begin{array}{l}\text { Expected Return } \\(\mathrm{NPV})\end{array} & \$ 160,000 & \$ 200,000 & \$ 125,000 & \$ 150,000 & \$ 225,000 \\\hline 6 & \begin{array}{l}\text { Cash } \\\text { requirements }\end{array} & \$ 45,000 & \$ 70,000 & \$ 28,000 & \$ 52,000 & \$ 65,000 &\$175,000\\\hline 7 & \begin{array}{l}\text { Personnel } \\\text { requirements }\end{array} & 7 & 4 & 2 & 6 & 4 & 10 \\\hline 8 & & & & & & & \\\hline 9 & \text { Model } \\\hline 10 & \\\hline 11 & \begin{array}{l}\text { Project selection } \\\text { decisions }\end{array} \\\hline 12 & \text { Cash Used } \\\hline 13 & \text { Personnel Used } \\\hline 14 & \text { Return } \\\hline\end{array}$

-What is the total amount of cash used for all five projects?

A) $ 175,000
B) $ 163,000
C) $ 215,000
D) $ 260,000

Question 39

Formulate and solve optimization models with binary variables and logical constraints.
Use the table below to answer the following question(s) by invoking the binary constraints on the variables using the standard Solver.
Below is the spreadsheet for a project selection model: $\begin{array}{|l|l|l|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\\hline & \text { Project Selection } & & & & & & \\1 & \text { Model } & & & & & & \\\hline 2 & & & & & & & \\\hline 3 & \text { Data } & & & & & & \\\hline 4 & & & & & & & \text { Available } \\ & & \text { Project 1 } & \text { Project 2 } & \text { Project 3 } & \text { Project 4 } & \text { Project 5 } & \text { Resources } \\\hline 5 & \begin{array}{l}\text { Expected Return } \\(\mathrm{NPV})\end{array} & \$ 160,000 & \$ 200,000 & \$ 125,000 & \$ 150,000 & \$ 225,000 \\\hline 6 & \begin{array}{l}\text { Cash } \\\text { requirements }\end{array} & \$ 45,000 & \$ 70,000 & \$ 28,000 & \$ 52,000 & \$ 65,000 &\$175,000\\\hline 7 & \begin{array}{l}\text { Personnel } \\\text { requirements }\end{array} & 7 & 4 & 2 & 6 & 4 & 10 \\\hline 8 & & & & & & & \\\hline 9 & \text { Model } \\\hline 10 & \\\hline 11 & \begin{array}{l}\text { Project selection } \\\text { decisions }\end{array} \\\hline 12 & \text { Cash Used } \\\hline 13 & \text { Personnel Used } \\\hline 14 & \text { Return } \\\hline\end{array}$

-What is the return obtained from Project 5?

A) $ 200,000
B) $ 125,000
C) $ 275,000
D) $ 225,000

Question 40

Formulate and solve optimization models with binary variables and logical constraints.
Use the table below to answer the following question(s) by invoking the binary constraints on the variables using the standard Solver.
Below is the spreadsheet for a project selection model: $\begin{array}{|l|l|l|l|l|l|l|l|}\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\\hline & \text { Project Selection } & & & & & & \\1 & \text { Model } & & & & & & \\\hline 2 & & & & & & & \\\hline 3 & \text { Data } & & & & & & \\\hline 4 & & & & & & & \text { Available } \\ & & \text { Project 1 } & \text { Project 2 } & \text { Project 3 } & \text { Project 4 } & \text { Project 5 } & \text { Resources } \\\hline 5 & \begin{array}{l}\text { Expected Return } \\(\mathrm{NPV})\end{array} & \$ 160,000 & \$ 200,000 & \$ 125,000 & \$ 150,000 & \$ 225,000 \\\hline 6 & \begin{array}{l}\text { Cash } \\\text { requirements }\end{array} & \$ 45,000 & \$ 70,000 & \$ 28,000 & \$ 52,000 & \$ 65,000 &\$175,000\\\hline 7 & \begin{array}{l}\text { Personnel } \\\text { requirements }\end{array} & 7 & 4 & 2 & 6 & 4 & 10 \\\hline 8 & & & & & & & \\\hline 9 & \text { Model } \\\hline 10 & \\\hline 11 & \begin{array}{l}\text { Project selection } \\\text { decisions }\end{array} \\\hline 12 & \text { Cash Used } \\\hline 13 & \text { Personnel Used } \\\hline 14 & \text { Return } \\\hline\end{array}$

-What is the total amount of personnel used for all five projects?

A) 23
B) 17
C) 10
D) 4

Question 41

To invoke the binary constraints on the variables, the option bin is chosen from the dropdown box in the Add Constraint dialog.

Question 42

Explain the method of solving models with general integer variables.

Question 43

What is the purpose of a heat map?

Question 44

What is the importance of binary variables in integer optimization models?

Question 45

If the Integer Tolerance is set to 0.01, the Solver will stop if it finds an integer solution that is within 10% of the optimal solution.

Question 46

Mathematically, a binary variable x can be represented as x > 2 and integer.

Question 47

Decision variables that are forced to be integers are called general integer variables.

Question 48

What is the importance of Integer Tolerance in Solver?

Question 49

Solver can generate a Sensitivity report for integer models.

Question 50

Explain the implementation of a project-selection model.