Deck 15: Integer Optimization
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Deck 15: Integer Optimization
1
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:
Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls.Answer the following questions using the standard Solver.Answer the following questions using the standard Solver.
What is the total scrap produced?
A)1,389
B)1,390
C)1,427
D)1,445
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:

Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls.Answer the following questions using the standard Solver.Answer the following questions using the standard Solver.
What is the total scrap produced?
A)1,389
B)1,390
C)1,427
D)1,445
B
2
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:
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
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:

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
C
3
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.

What is the total number of hours used for fabrication?
A)39.6
B)34.4
C)29.2
D)24.8

What is the total number of hours used for fabrication?
A)39.6
B)34.4
C)29.2
D)24.8
B
4
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:
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
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:

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
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5
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.

What is the quantity of Graystone surfboards produced?
A)2
B)5
C)7
D)10

What is the quantity of Graystone surfboards produced?
A)2
B)5
C)7
D)10
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6
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:

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
Below is the spreadsheet for a project selection model:

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
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7
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:
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 part-time employees needed for each 4-hour shift to ensure meeting the staffing requirements?
A)16
B)28
C)24
D)20
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:

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 part-time employees needed for each 4-hour shift to ensure meeting the staffing requirements?
A)16
B)28
C)24
D)20
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8
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
A)-1
B)0
C)0)5
D)1
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9
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.

What is the total profit generated?
A)$ 748.28
B)$ 687.46
C)$ 385.65
D)$ 500.00

What is the total profit generated?
A)$ 748.28
B)$ 687.46
C)$ 385.65
D)$ 500.00
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10
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:
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
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:

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
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11
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:
Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls.Answer the following questions using the standard Solver.Answer the following questions using the standard Solver.
What is the total number of 25-inch rolls produced?
A)630
B)635
C)641
D)645
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:

Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls.Answer the following questions using the standard Solver.Answer the following questions using the standard Solver.
What is the total number of 25-inch rolls produced?
A)630
B)635
C)641
D)645
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12
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.

Which of the following constraints is used in Solver?
A)$B$14:$C$14 = integer
B)$D$15 > = $D$6
C)$D$16 > = $D$7
D)$D$19 < = 0

Which of the following constraints is used in Solver?
A)$B$14:$C$14 = integer
B)$D$15 > = $D$6
C)$D$16 > = $D$7
D)$D$19 < = 0
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13
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:
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
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:

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
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14
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:
Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls.Answer the following questions using the standard Solver.Answer the following questions using the standard Solver.
What is the total number of 14-inch rolls produced?
A)721
B)725
C)726
D)740
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:

Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls.Answer the following questions using the standard Solver.Answer the following questions using the standard Solver.
What is the total number of 14-inch rolls produced?
A)721
B)725
C)726
D)740
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15
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:

What is the amount of cash used for Project 2?
A)$ 105,000
B)$ 25,000
C)$ 115,000
D)$ 70,000
Below is the spreadsheet for a project selection model:

What is the amount of cash used for Project 2?
A)$ 105,000
B)$ 25,000
C)$ 115,000
D)$ 70,000
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16
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.

What is the total number of hours used for the finishing operation?
A)39.6
B)34.4
C)29.2
D)24.8

What is the total number of hours used for the finishing operation?
A)39.6
B)34.4
C)29.2
D)24.8
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17
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.

What is the quantity of Lava surfboards produced?
A)2
B)5
C)7
D)10

What is the quantity of Lava surfboards produced?
A)2
B)5
C)7
D)10
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18
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:
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.
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:

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.
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19
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:
Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls.Answer the following questions using the standard Solver.Answer the following questions using the standard Solver.
What is the total number of 10-inch rolls produced?
A)940
B)946
C)950
D)960
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:

Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls.Answer the following questions using the standard Solver.Answer the following questions using the standard Solver.
What is the total number of 10-inch rolls produced?
A)940
B)946
C)950
D)960
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20
________ is the parameter that specifies when the Solver algorithm will terminate.
A)Mutation Rate
B)Population Size
C)Integer Tolerance
D)Convergence
A)Mutation Rate
B)Population Size
C)Integer Tolerance
D)Convergence
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21
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for Memphis Designs fixed cost model:

What is the net production at the end of the third quarter?
A)75
B)200
C)450
D)600
Below is the spreadsheet for Memphis Designs fixed cost model:

What is the net production at the end of the third quarter?
A)75
B)200
C)450
D)600
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22
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:

What is the return obtained from Project 5?
A)$ 200,000
B)$ 125,000
C)$ 275,000
D)$ 225,000
Below is the spreadsheet for a project selection model:

What is the return obtained from Project 5?
A)$ 200,000
B)$ 125,000
C)$ 275,000
D)$ 225,000
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23
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for Memphis Designs fixed cost model:

What is the net production at the end of the second quarter?
A)75
B)200
C)450
D)600
Below is the spreadsheet for Memphis Designs fixed cost model:

What is the net production at the end of the second quarter?
A)75
B)200
C)450
D)600
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24
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for a plant location model:

What is the total amount shipped by the Atlanta plant to the distribution centers?
A)750
B)1,000
C)1,250
D)1,300
Below is the spreadsheet for a plant location model:

What is the total amount shipped by the Atlanta plant to the distribution centers?
A)750
B)1,000
C)1,250
D)1,300
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25
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:

What is the amount of personnel used for Project 2?
A)3
B)4
C)6
D)11
Below is the spreadsheet for a project selection model:

What is the amount of personnel used for Project 2?
A)3
B)4
C)6
D)11
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26
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for a plant location model:

Which of the following constraints is used in Solver?
A)$F$16:$F$17 >= $F$6:$F$7
B)$B$20:$E$20 >= $B$10:$E$10
C)$B$18:$E$18 = binary
D)$J$16:$J$17 > = 0
Below is the spreadsheet for a plant location model:

Which of the following constraints is used in Solver?
A)$F$16:$F$17 >= $F$6:$F$7
B)$B$20:$E$20 >= $B$10:$E$10
C)$B$18:$E$18 = binary
D)$J$16:$J$17 > = 0
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27
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for a plant location model:

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
Below is the spreadsheet for a plant location model:

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
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28
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:

What is the total amount of personnel used for all five projects?
A)23
B)17
C)10
D)4
Below is the spreadsheet for a project selection model:

What is the total amount of personnel used for all five projects?
A)23
B)17
C)10
D)4
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29
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for Memphis Designs fixed cost model:

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$8
D)$C$15:$D$15 = binary
Below is the spreadsheet for Memphis Designs fixed cost model:

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$8
D)$C$15:$D$15 = binary
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30
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for a plant location model:

What is the total amount shipped by the Dallas plant to the distribution centers?
A)750
B)1,000
C)1,250
D)1,300
Below is the spreadsheet for a plant location model:

What is the total amount shipped by the Dallas plant to the distribution centers?
A)750
B)1,000
C)1,250
D)1,300
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31
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for a plant location model:

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
Below is the spreadsheet for a plant location model:

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
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32
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:

What is the return obtained from Project 3?
A)$ 200,000
B)$ 125,000
C)$ 275,000
D)$ 225,000
Below is the spreadsheet for a project selection model:

What is the return obtained from Project 3?
A)$ 200,000
B)$ 125,000
C)$ 275,000
D)$ 225,000
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33
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for Memphis Designs fixed cost model:

What is the inventory at the end of the first quarter?
A)600
B)400
C)50
D)75
Below is the spreadsheet for Memphis Designs fixed cost model:

What is the inventory at the end of the first quarter?
A)600
B)400
C)50
D)75
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34
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:

What is the amount of cash used for Project 5?
A)$ 65,000
B)$ 117,000
C)$ 13,000
D)$ 110,000
Below is the spreadsheet for a project selection model:

What is the amount of cash used for Project 5?
A)$ 65,000
B)$ 117,000
C)$ 13,000
D)$ 110,000
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35
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for a plant location model:

What is the total cost incurred?
A)$ 28,956
B)$ 35,233
C)$ 42,675
D)$ 47,864
Below is the spreadsheet for a plant location model:

What is the total cost incurred?
A)$ 28,956
B)$ 35,233
C)$ 42,675
D)$ 47,864
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36
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:

What is the total amount of cash used for all five projects?
A)$ 175,000
B)$ 163,000
C)$ 215,000
D)$ 260,000
Below is the spreadsheet for a project selection model:

What is the total amount of cash used for all five projects?
A)$ 175,000
B)$ 163,000
C)$ 215,000
D)$ 260,000
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37
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:

What is the total return obtained from all five projects?
A)$ 860,000
B)$ 550,000
C)$ 700,000
D)$ 395,000
Below is the spreadsheet for a project selection model:

What is the total return obtained from all five projects?
A)$ 860,000
B)$ 550,000
C)$ 700,000
D)$ 395,000
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38
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for Memphis Designs fixed cost model:

What is the net production at the end of the first quarter?
A)75
B)200
C)450
D)600
Below is the spreadsheet for Memphis Designs fixed cost model:

What is the net production at the end of the first quarter?
A)75
B)200
C)450
D)600
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39
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for Memphis Designs fixed cost model:

What is the binary constraint at the end of the third quarter?
A)75
B)200
C)450
D)600
Below is the spreadsheet for Memphis Designs fixed cost model:

What is the binary constraint at the end of the third quarter?
A)75
B)200
C)450
D)600
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40
Use the table below to answer the following question(s)using the standard Solver.
Below is the spreadsheet for Memphis Designs fixed cost model:

What is the total cost incurred by the company?
A)$ 8,637.50
B)$ 10,756.80
C)$ 7,289.62
D)$ 9,582.75
Below is the spreadsheet for Memphis Designs fixed cost model:

What is the total cost incurred by the company?
A)$ 8,637.50
B)$ 10,756.80
C)$ 7,289.62
D)$ 9,582.75
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41
What is the purpose of a heat map?
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42
Decision variables that are forced to be integers are called general integer variables.
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43
What is the importance of Integer Tolerance in Solver?
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44
What is the importance of binary variables in integer optimization models?
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45
Solver can generate a Sensitivity report for integer models.
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46
Mathematically, a binary variable x can be represented as x > 2 and integer.
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47
Explain the implementation of a project-selection model.
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48
Explain the method of solving models with general integer variables.
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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.
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50
To invoke the binary constraints on the variables, the option bin is chosen from the dropdown box in the Add Constraint dialog.
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