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

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

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

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

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

Exam 15: Integer Optimization

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: A B C D E F G Project Selection 1 Model 2 3 Data 4 Available Project 1 Project 2 Project 3 Project 4 Project 5 Resources 5 Expected Return () \ 160,000 \ 200,000 \ 125,000 \ 150,000 \ 225,000 6 Cash requirements \ 45,000 \ 70,000 \ 28,000 \ 52,000 \ 65,000 \1 75,000 7 Personnel requirements 7 4 2 6 4 10 8 9 Model 10 11 Project selection decisions 12 Cash Used 13 Personnel Used 14 Return -What is the amount of cash used for Project 2?

(Multiple Choice)

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Question 41

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: 1 Memphis Design Fixed Cost Model 2 3 Data 4 5 Cost Quarter 1 Quarter 2 Quarter 3 6 Production \ 10.00 \ 15.00 \ 13.50 7 Inventory \ 1.70 \ 1.70 \ 1.70 8 Demand 200 450 75 9 Fixed Cost \ 75.00 \ 75.00 \ 75.00 10 11 Model 12 13 Quarter 1 Quarter 2 Quarter 3 14 Production 15 Inventory 16 Binary 17 18 Binary constraints 19 Net Production 20 21 Cost 22 Total -What is the total cost incurred by the company?

(Multiple Choice)

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Question 42

Explain the method of solving models with general integer variables.

(Essay)

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Question 43

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: Hour Minimum Staff Required 8-9 6 9-10 10 10-11 12 11 -noon 10 noon-1 8 1-2 16 2-3 15 3-4 20 4-5 15 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?

(Multiple Choice)

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Question 44

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. A B C D 1 Stone Age Surfboards 2 3 Data 4 Product 5 Department Graystone Lava Limitations (hours) 6 Fabrication 2.5 4.2 74 7 Finishing 2 3.6 30 8 9 Profit/Unit \ 40.00 \ 60.00 10 11 12 Model 13 Graystone Lava 14 Quantity Produced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 Profit Contribution -What is the total number of hours used for the finishing operation?

(Multiple Choice)

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Question 45

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: 1 Memphis Design Fixed Cost Model 2 3 Data 4 5 Cost Quarter 1 Quarter 2 Quarter 3 6 Production \ 10.00 \ 15.00 \ 13.50 7 Inventory \ 1.70 \ 1.70 \ 1.70 8 Demand 200 450 75 9 Fixed Cost \ 75.00 \ 75.00 \ 75.00 10 11 Model 12 13 Quarter 1 Quarter 2 Quarter 3 14 Production 15 Inventory 16 Binary 17 18 Binary constraints 19 Net Production 20 21 Cost 22 Total -Which of the following constraints is used in Solver?

(Multiple Choice)

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Question 46

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

(True/False)

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Question 47

What is the importance of Integer Tolerance in Solver?

(Essay)

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Question 48

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: A B C D E F G Project Selection 1 Model 2 3 Data 4 Available Project 1 Project 2 Project 3 Project 4 Project 5 Resources 5 Expected Return () \ 160,000 \ 200,000 \ 125,000 \ 150,000 \ 225,000 6 Cash requirements \ 45,000 \ 70,000 \ 28,000 \ 52,000 \ 65,000 \1 75,000 7 Personnel requirements 7 4 2 6 4 10 8 9 Model 10 11 Project selection decisions 12 Cash Used 13 Personnel Used 14 Return -Which of the following cells is set as the objective cell in Solver?

(Multiple Choice)

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Question 49

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.

(True/False)

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Question 50

Explain the method of solving models with general integer variables.

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

What is the importance of Integer Tolerance in Solver?

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.

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