Deck 14: Integer and Nonlinear Optimization Models

Question 1

Use the table below to answer the following questions) 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: $$\begin{array} { | l | l| } \hline \text { Hour } & \text { Minimum Staff Required } \\\hline 8 - 9 & 6 \\\hline 9 - 10 & 10 \\\hline 10 - 11 & 12 \\\hline 11 - \text { noon } & 10 \\\hline noon - 1 & 8 \\\hline 1 - 2 & 16 \\\hline 2 - 3 & 15 \\\hline 3 - 4 & 20 \\\hline 4 - 5 & 15 \\\hline\end{array}$$ 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.

Answer 1

It is a general integer variable that is restricted to being between 0 and 1.

Question 2

Use the table below to answer the following questions) 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: $\begin{array}{|c|c|c|c|c|c|} \hline&{\text { A }} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \mathrm{E} \\\hline 1 & \text { Cutting-Stock Problem } & & & & \\\hline 2 & & & & & \\\hline 3 & \text { Data } & & & & \\\hline 4 & \text { Pattein } & \text { 10-in rolls } & \text { 14 in. rolls } & \text { 25-in. rolls } & \text { Scrap } \\\hline 5 & 1 & 0 & 8 & 0 & 10 \\\hline 6 & 2 & 0 & 2 & 3 & 10 \\\hline 7 & 3 & 3 & 0 & 3 & 4 \\\hline 8 & 4 & 10 & 0 & 0 & 10 \\\hline 9 & 5 & 3 & 2 & 2 & 4 \\\hline 10 & 6 & 8 & 2 & 0 & 4 \\\hline\end{array}$ 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

Answer 2

1,390

Question 3

Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models.
Use the spreadsheet below for Stone Age Surfboards to answer the following questions) 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

Answer 3

7

Question 4

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

Question 5

Use the table below to answer the following questions) 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: $\begin{array}{|c|c|c|c|c|c|} \hline&{\text { A }} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \mathrm{E} \\\hline 1 & \text { Cutting-Stock Problem } & & & & \\\hline 2 & & & & & \\\hline 3 & \text { Data } & & & & \\\hline 4 & \text { Pattein } & \text { 10-in rolls } & \text { 14 in. rolls } & \text { 25-in. rolls } & \text { Scrap } \\\hline 5 & 1 & 0 & 8 & 0 & 10 \\\hline 6 & 2 & 0 & 2 & 3 & 10 \\\hline 7 & 3 & 3 & 0 & 3 & 4 \\\hline 8 & 4 & 10 & 0 & 0 & 10 \\\hline 9 & 5 & 3 & 2 & 2 & 4 \\\hline 10 & 6 & 8 & 2 & 0 & 4 \\\hline\end{array}$ 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 6

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 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 works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models.
Use the spreadsheet below for Stone Age Surfboards to answer the following questions) 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

Question 8

Use the table below to answer the following questions) 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: $$\begin{array} { | l | l| } \hline \text { Hour } & \text { Minimum Staff Required } \\\hline 8 - 9 & 6 \\\hline 9 - 10 & 10 \\\hline 10 - 11 & 12 \\\hline 11 - \text { noon } & 10 \\\hline noon - 1 & 8 \\\hline 1 - 2 & 16 \\\hline 2 - 3 & 15 \\\hline 3 - 4 & 20 \\\hline 4 - 5 & 15 \\\hline\end{array}$$ 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 9

Use the table below to answer the following questions) 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: $\begin{array}{|c|c|c|c|c|c|} \hline&{\text { A }} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \mathrm{E} \\\hline 1 & \text { Cutting-Stock Problem } & & & & \\\hline 2 & & & & & \\\hline 3 & \text { Data } & & & & \\\hline 4 & \text { Pattein } & \text { 10-in rolls } & \text { 14 in. rolls } & \text { 25-in. rolls } & \text { Scrap } \\\hline 5 & 1 & 0 & 8 & 0 & 10 \\\hline 6 & 2 & 0 & 2 & 3 & 10 \\\hline 7 & 3 & 3 & 0 & 3 & 4 \\\hline 8 & 4 & 10 & 0 & 0 & 10 \\\hline 9 & 5 & 3 & 2 & 2 & 4 \\\hline 10 & 6 & 8 & 2 & 0 & 4 \\\hline\end{array}$ 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 10

Use the table below to answer the following questions) 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: $\begin{array}{|c|c|c|c|c|c|} \hline&{\text { A }} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \mathrm{E} \\\hline 1 & \text { Cutting-Stock Problem } & & & & \\\hline 2 & & & & & \\\hline 3 & \text { Data } & & & & \\\hline 4 & \text { Pattein } & \text { 10-in rolls } & \text { 14 in. rolls } & \text { 25-in. rolls } & \text { Scrap } \\\hline 5 & 1 & 0 & 8 & 0 & 10 \\\hline 6 & 2 & 0 & 2 & 3 & 10 \\\hline 7 & 3 & 3 & 0 & 3 & 4 \\\hline 8 & 4 & 10 & 0 & 0 & 10 \\\hline 9 & 5 & 3 & 2 & 2 & 4 \\\hline 10 & 6 & 8 & 2 & 0 & 4 \\\hline\end{array}$ 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 11

Use the table below to answer the following questions) 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: $$\begin{array} { | l | l| } \hline \text { Hour } & \text { Minimum Staff Required } \\\hline 8 - 9 & 6 \\\hline 9 - 10 & 10 \\\hline 10 - 11 & 12 \\\hline 11 - \text { noon } & 10 \\\hline noon - 1 & 8 \\\hline 1 - 2 & 16 \\\hline 2 - 3 & 15 \\\hline 3 - 4 & 20 \\\hline 4 - 5 & 15 \\\hline\end{array}$$ 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 12

Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models.
Use the spreadsheet below for Stone Age Surfboards to answer the following questions) 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

Question 13

Use the table below to answer the following questions) 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: $$\begin{array} { | l | l| } \hline \text { Hour } & \text { Minimum Staff Required } \\\hline 8 - 9 & 6 \\\hline 9 - 10 & 10 \\\hline 10 - 11 & 12 \\\hline 11 - \text { noon } & 10 \\\hline noon - 1 & 8 \\\hline 1 - 2 & 16 \\\hline 2 - 3 & 15 \\\hline 3 - 4 & 20 \\\hline 4 - 5 & 15 \\\hline\end{array}$$ 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

Question 14

Use the table below to answer the following questions) 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: $$\begin{array} { | l | l| } \hline \text { Hour } & \text { Minimum Staff Required } \\\hline 8 - 9 & 6 \\\hline 9 - 10 & 10 \\\hline 10 - 11 & 12 \\\hline 11 - \text { noon } & 10 \\\hline noon - 1 & 8 \\\hline 1 - 2 & 16 \\\hline 2 - 3 & 15 \\\hline 3 - 4 & 20 \\\hline 4 - 5 & 15 \\\hline\end{array}$$ 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 15

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

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

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

Question 16

Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models.
Use the spreadsheet below for Stone Age Surfboards to answer the following questions) 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

Question 17

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

-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 18

Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models.
Use the spreadsheet below for Stone Age Surfboards to answer the following questions) 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

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 works
9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models.
Use the spreadsheet below for Stone Age Surfboards to answer the following questions) using integer constraints on variables in the optimization models using the standard Solver.
Which of the following constraints does Solver use?

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

Question 20

Use the table below to answer the following questions) 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: $$\begin{array} { | l | l| } \hline \text { Hour } & \text { Minimum Staff Required } \\\hline 8 - 9 & 6 \\\hline 9 - 10 & 10 \\\hline 10 - 11 & 12 \\\hline 11 - \text { noon } & 10 \\\hline noon - 1 & 8 \\\hline 1 - 2 & 16 \\\hline 2 - 3 & 15 \\\hline 3 - 4 & 20 \\\hline 4 - 5 & 15 \\\hline\end{array}$$ 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 21

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

Question 22

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 23

Use the table below to create a nonlinear model based on the table to answer the following questions).
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. $$\begin{array} {| l | l | l | l | l | l | l | } \hline \begin{array} { l } \text { Atlas Mavie } \\\text { Theater } \\\text { Ticketing }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & & & \\\hline & & & & & & \\\hline \text { Ticket Class } & \begin{array} { l } \text { Current } \\\text { Rate }\end{array} & \begin{array} { l } \text { Avernge } \\\text { Daily } \\\text { Sald }\end{array} & \text { Elasticity } & \begin{array} { l } \text { Tatal } \\\text { Seating } \\\text { Capacity }\end{array} & { \text { Price Range } } \\\hline \text { Classic } & \$ 8.45 & 150 & - 1.5 & 300 & \$ 6.50 & \$ 7.50 \\\hline \text { Silver } & \$ 13.25 & \mathbf { 8 0 } & - 2 & & \$ 1.50 & \$ 12.50 \\\hline \text { Gald } & \$ 17.50 & \mathbf { 3 0 } & - 1 & & \$ 15.50 & \$ 16.50 \\\hline\end{array}$$

-According to the nonlinear model, what is the new price for Classic tickets?

A) $7.50
B) $12.45
C) $6.50
D) $8.20

Question 24

Use the table below to answer the following questions). $\begin{array}{|l|l|}\hline \text { Bolton Computer's } & \\\text { Laptop } & \\\text { Pricing Decision } & \\\hline & \\\hline \text { Inputs } & \\\hline \\\hline \text { Price }\\\hline \\\hline \text { model }\\\hline \\\hline \text { sales }&-3.85 \times price+1150.9\\\hline \\\hline \text {outputs }\\\hline \\\hline \text { total revenue }&\text { sales }\times \text {price }\\\hline\end{array}$

-According to the nonlinear model, which of the following is the total revenue expected from the sales?

A) 22,340.91
B) 86,011.09
C) 107,571.78
D) 74,733.77

Question 25

Use the table below to answer the following questions). $\begin{array}{|l|l|}\hline \text { Bolton Computer's } & \\\text { Laptop } & \\\text { Pricing Decision } & \\\hline & \\\hline \text { Inputs } & \\\hline \\\hline \text { Price }\\\hline \\\hline \text { model }\\\hline \\\hline \text { sales }&-3.85 \times price+1150.9\\\hline \\\hline \text {outputs }\\\hline \\\hline \text { total revenue }&\text { sales }\times \text {price }\\\hline\end{array}$

-According to the nonlinear model, which of the following is the expected sales figure based on the computed price?

A) 149.47
B) 719.7
C) 575.45
D) 500

Question 26

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

Question 27

What is the return obtained from Project 3?

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

Question 28

What is the total return obtained from all five projects?

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

Question 29

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

Question 30

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

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

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

Question 31

Use the table below to create a nonlinear model based on the table to answer the following questions).
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. $$\begin{array} {| l | l | l | l | l | l | l | } \hline \begin{array} { l } \text { Atlas Mavie } \\\text { Theater } \\\text { Ticketing }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & & & \\\hline & & & & & & \\\hline \text { Ticket Class } & \begin{array} { l } \text { Current } \\\text { Rate }\end{array} & \begin{array} { l } \text { Avernge } \\\text { Daily } \\\text { Sald }\end{array} & \text { Elasticity } & \begin{array} { l } \text { Tatal } \\\text { Seating } \\\text { Capacity }\end{array} & { \text { Price Range } } \\\hline \text { Classic } & \$ 8.45 & 150 & - 1.5 & 300 & \$ 6.50 & \$ 7.50 \\\hline \text { Silver } & \$ 13.25 & \mathbf { 8 0 } & - 2 & & \$ 1.50 & \$ 12.50 \\\hline \text { Gald } & \$ 17.50 & \mathbf { 3 0 } & - 1 & & \$ 15.50 & \$ 16.50 \\\hline\end{array}$$

-According to the nonlinear model, what is the new price for Gold tickets?

A) $16.50
B) $15.50
C) $16
D) $16.11

Question 32

Use the table below to create a nonlinear model based on the table to answer the following questions).
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. $$\begin{array} {| l | l | l | l | l | l | l | } \hline \begin{array} { l } \text { Atlas Mavie } \\\text { Theater } \\\text { Ticketing }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & & & \\\hline & & & & & & \\\hline \text { Ticket Class } & \begin{array} { l } \text { Current } \\\text { Rate }\end{array} & \begin{array} { l } \text { Avernge } \\\text { Daily } \\\text { Sald }\end{array} & \text { Elasticity } & \begin{array} { l } \text { Tatal } \\\text { Seating } \\\text { Capacity }\end{array} & { \text { Price Range } } \\\hline \text { Classic } & \$ 8.45 & 150 & - 1.5 & 300 & \$ 6.50 & \$ 7.50 \\\hline \text { Silver } & \$ 13.25 & \mathbf { 8 0 } & - 2 & & \$ 1.50 & \$ 12.50 \\\hline \text { Gald } & \$ 17.50 & \mathbf { 3 0 } & - 1 & & \$ 15.50 & \$ 16.50 \\\hline\end{array}$$

-According to the nonlinear model, what is the new price for Silver tickets?

A) $7.40
B) $12.17
C) $11.50
D) $12.50

Question 33

What is the importance of Integer Tolerance in Solver?

Question 34

Explain the method of Integer Linear Optimization Models.

Question 35

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

-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 36

What is the return obtained from Project 5?

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

Question 37

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

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

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

Question 38

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

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

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

Question 39

Use the table below to create a nonlinear model based on the table to answer the following questions).
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. $$\begin{array} {| l | l | l | l | l | l | l | } \hline \begin{array} { l } \text { Atlas Mavie } \\\text { Theater } \\\text { Ticketing }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & & & \\\hline & & & & & & \\\hline \text { Ticket Class } & \begin{array} { l } \text { Current } \\\text { Rate }\end{array} & \begin{array} { l } \text { Avernge } \\\text { Daily } \\\text { Sald }\end{array} & \text { Elasticity } & \begin{array} { l } \text { Tatal } \\\text { Seating } \\\text { Capacity }\end{array} & { \text { Price Range } } \\\hline \text { Classic } & \$ 8.45 & 150 & - 1.5 & 300 & \$ 6.50 & \$ 7.50 \\\hline \text { Silver } & \$ 13.25 & \mathbf { 8 0 } & - 2 & & \$ 1.50 & \$ 12.50 \\\hline \text { Gald } & \$ 17.50 & \mathbf { 3 0 } & - 1 & & \$ 15.50 & \$ 16.50 \\\hline\end{array}$$

-According to the nonlinear model, which of the following is the projected sales figure for Classic tickets at the new price?

A) 32
B) 90
C) 175
D) 202

Question 40

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

Question 41

Use the table below to create a nonlinear model based on the table to answer the following questions).
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. $$\begin{array} {| l | l | l | l | l | l | l | } \hline \begin{array} { l } \text { Atlas Mavie } \\\text { Theater } \\\text { Ticketing }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & & & \\\hline & & & & & & \\\hline \text { Ticket Class } & \begin{array} { l } \text { Current } \\\text { Rate }\end{array} & \begin{array} { l } \text { Avernge } \\\text { Daily } \\\text { Sald }\end{array} & \text { Elasticity } & \begin{array} { l } \text { Tatal } \\\text { Seating } \\\text { Capacity }\end{array} & { \text { Price Range } } \\\hline \text { Classic } & \$ 8.45 & 150 & - 1.5 & 300 & \$ 6.50 & \$ 7.50 \\\hline \text { Silver } & \$ 13.25 & \mathbf { 8 0 } & - 2 & & \$ 1.50 & \$ 12.50 \\\hline \text { Gald } & \$ 17.50 & \mathbf { 3 0 } & - 1 & & \$ 15.50 & \$ 16.50 \\\hline\end{array}$$

-According to the nonlinear model, which of the following is the total projected revenue for the new sales figures?

A) $1,637.72
B) $2,970.09
C) $1,316.92
D) $2,865.89

Question 42

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the distance between Shirley's new accommodation and Bungalow 5?

A) 54.62
B) 25.08
C) 14.53
D) 91.16

Question 43

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the distance between Shirley's new accommodation and Bungalow 2?

A) 91.16
B) 23.12
C) 98.21
D) 14.53

Question 44

Use the table below to create a nonlinear model based on the table to answer the following questions).
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. $$\begin{array} {| l | l | l | l | l | l | l | } \hline \begin{array} { l } \text { Atlas Mavie } \\\text { Theater } \\\text { Ticketing }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & & & \\\hline & & & & & & \\\hline \text { Ticket Class } & \begin{array} { l } \text { Current } \\\text { Rate }\end{array} & \begin{array} { l } \text { Avernge } \\\text { Daily } \\\text { Sald }\end{array} & \text { Elasticity } & \begin{array} { l } \text { Tatal } \\\text { Seating } \\\text { Capacity }\end{array} & { \text { Price Range } } \\\hline \text { Classic } & \$ 8.45 & 150 & - 1.5 & 300 & \$ 6.50 & \$ 7.50 \\\hline \text { Silver } & \$ 13.25 & \mathbf { 8 0 } & - 2 & & \$ 1.50 & \$ 12.50 \\\hline \text { Gald } & \$ 17.50 & \mathbf { 3 0 } & - 1 & & \$ 15.50 & \$ 16.50 \\\hline\end{array}$$

-Which of the following is true of the nonlinear model created for the Atlas movie ticket repricing scenario?

A) The projected revenue for the Gold class is infeasible within the price range provided.
B) The projected value for most tickets sold is for the Silver class.
C) The total projected tickets sold exceed the total seating capacity.
D) The projected revenue is lowest for the Gold tickets.

Question 45

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 3?

A) 3152.08
B) 1529.39
C) 346.77
D) 250.78

Question 46

Use the table below to create a nonlinear model based on the table to answer the following questions).
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. $$\begin{array} {| l | l | l | l | l | l | l | } \hline \begin{array} { l } \text { Atlas Mavie } \\\text { Theater } \\\text { Ticketing }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & & & \\\hline & & & & & & \\\hline \text { Ticket Class } & \begin{array} { l } \text { Current } \\\text { Rate }\end{array} & \begin{array} { l } \text { Avernge } \\\text { Daily } \\\text { Sald }\end{array} & \text { Elasticity } & \begin{array} { l } \text { Tatal } \\\text { Seating } \\\text { Capacity }\end{array} & { \text { Price Range } } \\\hline \text { Classic } & \$ 8.45 & 150 & - 1.5 & 300 & \$ 6.50 & \$ 7.50 \\\hline \text { Silver } & \$ 13.25 & \mathbf { 8 0 } & - 2 & & \$ 1.50 & \$ 12.50 \\\hline \text { Gald } & \$ 17.50 & \mathbf { 3 0 } & - 1 & & \$ 15.50 & \$ 16.50 \\\hline\end{array}$$

-According to the nonlinear model, which of the following is the projected revenue figure for Classic tickets based on its new price?

A) $1,314.72
B) $1,116.03
C) $521.68
D) $1,312.52

Question 47

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the distance between Shirley's new accommodation and Bungalow 4?

A) 14.53
B) 250.78
C) 54.62
D) 98.21

Question 48

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the X-coordinate for the location of Shirley's new accommodation?

A) 54.62
B) 36.53
C) 25
D) 23.12

Question 49

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 5?

A) 435.89
B) 1529.39
C) 589.25
D) 250.78

Question 50

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 2?

A) 435.89
B) 250.78
C) 1529.39
D) 589.25

Question 51

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 4?

A) 589.25
B) 346.77
C) 1529.39
D) 3152.08

Question 52

Use the table below to create a nonlinear model based on the table to answer the following questions).
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. $$\begin{array} {| l | l | l | l | l | l | l | } \hline \begin{array} { l } \text { Atlas Mavie } \\\text { Theater } \\\text { Ticketing }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & & & \\\hline & & & & & & \\\hline \text { Ticket Class } & \begin{array} { l } \text { Current } \\\text { Rate }\end{array} & \begin{array} { l } \text { Avernge } \\\text { Daily } \\\text { Sald }\end{array} & \text { Elasticity } & \begin{array} { l } \text { Tatal } \\\text { Seating } \\\text { Capacity }\end{array} & { \text { Price Range } } \\\hline \text { Classic } & \$ 8.45 & 150 & - 1.5 & 300 & \$ 6.50 & \$ 7.50 \\\hline \text { Silver } & \$ 13.25 & \mathbf { 8 0 } & - 2 & & \$ 1.50 & \$ 12.50 \\\hline \text { Gald } & \$ 17.50 & \mathbf { 3 0 } & - 1 & & \$ 15.50 & \$ 16.50 \\\hline\end{array}$$

-According to the nonlinear model, which of the following is the projected sales figure for Silver tickets at the new price?

A) 93
B) 178
C) 202
D) 101

Question 53

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the distance between Shirley's new accommodation and Bungalow 3?

A) 54.62
B) 25.08
C) 36.53
D) 23.12

Question 54

Use the table below to create a nonlinear model based on the table to answer the following questions).
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. $$\begin{array} {| l | l | l | l | l | l | l | } \hline \begin{array} { l } \text { Atlas Mavie } \\\text { Theater } \\\text { Ticketing }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & & & \\\hline & & & & & & \\\hline \text { Ticket Class } & \begin{array} { l } \text { Current } \\\text { Rate }\end{array} & \begin{array} { l } \text { Avernge } \\\text { Daily } \\\text { Sald }\end{array} & \text { Elasticity } & \begin{array} { l } \text { Tatal } \\\text { Seating } \\\text { Capacity }\end{array} & { \text { Price Range } } \\\hline \text { Classic } & \$ 8.45 & 150 & - 1.5 & 300 & \$ 6.50 & \$ 7.50 \\\hline \text { Silver } & \$ 13.25 & \mathbf { 8 0 } & - 2 & & \$ 1.50 & \$ 12.50 \\\hline \text { Gald } & \$ 17.50 & \mathbf { 3 0 } & - 1 & & \$ 15.50 & \$ 16.50 \\\hline\end{array}$$

-Which of the following is the rectilinear distance between the points A13,15) and B10,12)?

A) 4
B) 25
C) 6
D) 10

Question 55

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the distance between Shirley's new accommodation and Bungalow 1?

A) 36.53
B) 14.53
C) 98.21
D) 23.12

Question 56

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the Y-coordinate for the location of Shirley's new accommodation?

A) 91.16
B) 25.08
C) 98.21
D) 54.62

Question 57

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 1?

A) 589.25
B) 435.89
C) 346.77
D) 3152.08

Question 58

Use the table below to create a nonlinear model based on the table to answer the following questions).
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. $$\begin{array} {| l | l | l | l | l | l | l | } \hline \begin{array} { l } \text { Atlas Mavie } \\\text { Theater } \\\text { Ticketing }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & & & \\\hline & & & & & & \\\hline \text { Ticket Class } & \begin{array} { l } \text { Current } \\\text { Rate }\end{array} & \begin{array} { l } \text { Avernge } \\\text { Daily } \\\text { Sald }\end{array} & \text { Elasticity } & \begin{array} { l } \text { Tatal } \\\text { Seating } \\\text { Capacity }\end{array} & { \text { Price Range } } \\\hline \text { Classic } & \$ 8.45 & 150 & - 1.5 & 300 & \$ 6.50 & \$ 7.50 \\\hline \text { Silver } & \$ 13.25 & \mathbf { 8 0 } & - 2 & & \$ 1.50 & \$ 12.50 \\\hline \text { Gald } & \$ 17.50 & \mathbf { 3 0 } & - 1 & & \$ 15.50 & \$ 16.50 \\\hline\end{array}$$

-According to the nonlinear model, which of the following is the projected sales figure for Gold tickets at the new price?

A) 32
B) 90
C) 33
D) 178

Question 59

Use the table below to create a nonlinear model based on the table to answer the following questions).
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. $$\begin{array} {| l | l | l | l | l | l | l | } \hline \begin{array} { l } \text { Atlas Mavie } \\\text { Theater } \\\text { Ticketing }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & & & \\\hline & & & & & & \\\hline \text { Ticket Class } & \begin{array} { l } \text { Current } \\\text { Rate }\end{array} & \begin{array} { l } \text { Avernge } \\\text { Daily } \\\text { Sald }\end{array} & \text { Elasticity } & \begin{array} { l } \text { Tatal } \\\text { Seating } \\\text { Capacity }\end{array} & { \text { Price Range } } \\\hline \text { Classic } & \$ 8.45 & 150 & - 1.5 & 300 & \$ 6.50 & \$ 7.50 \\\hline \text { Silver } & \$ 13.25 & \mathbf { 8 0 } & - 2 & & \$ 1.50 & \$ 12.50 \\\hline \text { Gald } & \$ 17.50 & \mathbf { 3 0 } & - 1 & & \$ 15.50 & \$ 16.50 \\\hline\end{array}$$

-According to the nonlinear model, which of the following is the projected revenue figure for Silver tickets based on its new price?

A) $1,163.02
B) $1,132.08
C) $1,224.63
D) $1,316.92

Question 60

Use the table below to create a nonlinear model based on the table to answer the following questions).
The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. $$\begin{array} {| l | l | l | l | l | l | l | } \hline \begin{array} { l } \text { Atlas Mavie } \\\text { Theater } \\\text { Ticketing }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & & & \\\hline & & & & & & \\\hline \text { Ticket Class } & \begin{array} { l } \text { Current } \\\text { Rate }\end{array} & \begin{array} { l } \text { Avernge } \\\text { Daily } \\\text { Sald }\end{array} & \text { Elasticity } & \begin{array} { l } \text { Tatal } \\\text { Seating } \\\text { Capacity }\end{array} & { \text { Price Range } } \\\hline \text { Classic } & \$ 8.45 & 150 & - 1.5 & 300 & \$ 6.50 & \$ 7.50 \\\hline \text { Silver } & \$ 13.25 & \mathbf { 8 0 } & - 2 & & \$ 1.50 & \$ 12.50 \\\hline \text { Gald } & \$ 17.50 & \mathbf { 3 0 } & - 1 & & \$ 15.50 & \$ 16.50 \\\hline\end{array}$$

-According to the nonlinear model, which of the following is the projected revenue figure for Gold tickets based on its new price?

A) $432.93
B) $1,316.92
C) $1,116.03
D) $523.29

Question 61

LO1: Develop and solve nonlinear optimization models for different applications. Use the table below to answer the following questions).
Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.
The table below provides the relevant information. $\begin{array}{|l|l|l|l|}\hline\text { Pickson Luthiers } \\ \text { Corporation } & \text { Phone Recharging Points } & \\\hline & & & \\\hline \text { Data } & \\\hline\\\hline \text { Cell } & X \text {-coordinate } & Y \text {-coordinate } & \text { Demand } \\\hline \text { Measurements } & 2 & 5 & 27 \\\hline \text { Paint } & 1 & 3 & 12 \\\hline \text { Electricals } & 4 & 2 & 25 \\\hline\end{array}$ $$\begin{array} { | l | l | l | l | } \hline \text { Testing } & 3.5 & 5 & 5 \\\hline \text { Packnging } & 3 & 3 & 7 \\\hline & & & \\\hline \text { Maxirnum } & 4 & 5 & \\\hline\end{array}$$ The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.
Create a nonsmooth optimization model, based on the data, to answer the following questions. Hint: Choose the closest answers.)

-According to the model, which of the following is the Y-coordinate for the phone charger location?

A) 1.50
B) 1.00
C) 3.00
D) 5.00

Question 62

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, what is the total weighted distance that Shirley would travel between the bungalows?

A) 4151.29
B) 1529.39
C) 3152.08
D) 4305.30

Question 63

Use the table below to answer the following questions).
Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%. $$\begin{array} { | l | r | l | l | l | l | r | } \hline \begin{array} { l } \text { Reese's Stuck } \\\text { Investment } \\\text { Plan }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & \\\hline & \text { Expected } & & & { \text { Variance-Covariance Matrix } } \\\hline & \text { Return } & & & \text { Stack 1 } & \text { Stack 2 } & \text { Stack 3 } \\\hline \text { Stack 1 } & 10 \% & & \text { Stack 1 } & 0.021 & 0.018 & - 0.003 \\\hline \text { Stack 2 } & 11 \% & & \text { Stack 2 } & 0.018 & 0.070 & 0.006 \\\hline \text { Stack 3 } & 9 \% & & \text { Stack 3 } & - 0.003 & 0.006 & 0.003 \\\hline \begin{array} { l } \text { Target } \\\text { Retum }\end{array} & 10 \% & & & & & \\\hline\end{array}$$ Develop a Nonlinear Optimization Models model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.

-According to the model, what is the cross-product value for Stock 1 variance?

A) 0.00176
B) 0.00450
C) -0.00047
D) 0.00194

Question 64

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-Given that Q = order quantity, D = annual demand, C = unit cost of the item, C0 = cost per order placed, i = inventory carrying charge per unit, which of the following represents the holding cost per unit?

A) D/Q
B) iC
C) D/Q)C0
D) iCQ/2

Question 65

Use the table below to answer the following questions).
Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%. $$\begin{array} { | l | r | l | l | l | l | r | } \hline \begin{array} { l } \text { Reese's Stuck } \\\text { Investment } \\\text { Plan }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & \\\hline & \text { Expected } & & & { \text { Variance-Covariance Matrix } } \\\hline & \text { Return } & & & \text { Stack 1 } & \text { Stack 2 } & \text { Stack 3 } \\\hline \text { Stack 1 } & 10 \% & & \text { Stack 1 } & 0.021 & 0.018 & - 0.003 \\\hline \text { Stack 2 } & 11 \% & & \text { Stack 2 } & 0.018 & 0.070 & 0.006 \\\hline \text { Stack 3 } & 9 \% & & \text { Stack 3 } & - 0.003 & 0.006 & 0.003 \\\hline \begin{array} { l } \text { Target } \\\text { Retum }\end{array} & 10 \% & & & & & \\\hline\end{array}$$ Develop a Nonlinear Optimization Models model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.

-According to the model, what percentage of the budget should be allocated to Stock 1?

A) 10%
B) 25%
C) 50%
D) 40%

Question 66

LO1: Develop and solve nonlinear optimization models for different applications. Use the table below to answer the following questions).
Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.
The table below provides the relevant information. $\begin{array}{|l|l|l|l|}\hline\text { Pickson Luthiers } \\ \text { Corporation } & \text { Phone Recharging Points } & \\\hline & & & \\\hline \text { Data } & \\\hline\\\hline \text { Cell } & X \text {-coordinate } & Y \text {-coordinate } & \text { Demand } \\\hline \text { Measurements } & 2 & 5 & 27 \\\hline \text { Paint } & 1 & 3 & 12 \\\hline \text { Electricals } & 4 & 2 & 25 \\\hline\end{array}$ $$\begin{array} { | l | l | l | l | } \hline \text { Testing } & 3.5 & 5 & 5 \\\hline \text { Packnging } & 3 & 3 & 7 \\\hline & & & \\\hline \text { Maxirnum } & 4 & 5 & \\\hline\end{array}$$ The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.
Create a nonsmooth optimization model, based on the data, to answer the following questions. Hint: Choose the closest answers.)

-According to the model, which of the following is the weighted distance between the phone charger and Measurements cell?

A) 12.00
B) 75.00
C) 7.00
D) 54.00

Question 67

Use the table below to answer the following questions).
Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%. $$\begin{array} { | l | r | l | l | l | l | r | } \hline \begin{array} { l } \text { Reese's Stuck } \\\text { Investment } \\\text { Plan }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & \\\hline & \text { Expected } & & & { \text { Variance-Covariance Matrix } } \\\hline & \text { Return } & & & \text { Stack 1 } & \text { Stack 2 } & \text { Stack 3 } \\\hline \text { Stack 1 } & 10 \% & & \text { Stack 1 } & 0.021 & 0.018 & - 0.003 \\\hline \text { Stack 2 } & 11 \% & & \text { Stack 2 } & 0.018 & 0.070 & 0.006 \\\hline \text { Stack 3 } & 9 \% & & \text { Stack 3 } & - 0.003 & 0.006 & 0.003 \\\hline \begin{array} { l } \text { Target } \\\text { Retum }\end{array} & 10 \% & & & & & \\\hline\end{array}$$ Develop a Nonlinear Optimization Models model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.

-According to the model, what is the cross-product value for Stock 2 variance?

A) 0.00080
B) -0.00080
C) -0.00075
D) 0.01132

Question 68

LO1: Develop and solve nonlinear optimization models for different applications. Use the table below to answer the following questions).
Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.
The table below provides the relevant information. $\begin{array}{|l|l|l|l|}\hline\text { Pickson Luthiers } \\ \text { Corporation } & \text { Phone Recharging Points } & \\\hline & & & \\\hline \text { Data } & \\\hline\\\hline \text { Cell } & X \text {-coordinate } & Y \text {-coordinate } & \text { Demand } \\\hline \text { Measurements } & 2 & 5 & 27 \\\hline \text { Paint } & 1 & 3 & 12 \\\hline \text { Electricals } & 4 & 2 & 25 \\\hline\end{array}$ $$\begin{array} { | l | l | l | l | } \hline \text { Testing } & 3.5 & 5 & 5 \\\hline \text { Packnging } & 3 & 3 & 7 \\\hline & & & \\\hline \text { Maxirnum } & 4 & 5 & \\\hline\end{array}$$ The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.
Create a nonsmooth optimization model, based on the data, to answer the following questions. Hint: Choose the closest answers.)

-According to the model, which of the following is the X-coordinate for the phone charger location?

A) 2.00
B) 3.00
C) 3.50
D) 4.00

Question 69

Use the table below to answer the following questions).
Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%. $$\begin{array} { | l | r | l | l | l | l | r | } \hline \begin{array} { l } \text { Reese's Stuck } \\\text { Investment } \\\text { Plan }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & \\\hline & \text { Expected } & & & { \text { Variance-Covariance Matrix } } \\\hline & \text { Return } & & & \text { Stack 1 } & \text { Stack 2 } & \text { Stack 3 } \\\hline \text { Stack 1 } & 10 \% & & \text { Stack 1 } & 0.021 & 0.018 & - 0.003 \\\hline \text { Stack 2 } & 11 \% & & \text { Stack 2 } & 0.018 & 0.070 & 0.006 \\\hline \text { Stack 3 } & 9 \% & & \text { Stack 3 } & - 0.003 & 0.006 & 0.003 \\\hline \begin{array} { l } \text { Target } \\\text { Retum }\end{array} & 10 \% & & & & & \\\hline\end{array}$$ Develop a Nonlinear Optimization Models model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.

-According to the model, what percentage of the budget should be allocated to Stock 3?

A) 40%
B) 20%
C) 25%
D) 75%

Question 70

Use the table below to answer the following questions).
Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%. $$\begin{array} { | l | r | l | l | l | l | r | } \hline \begin{array} { l } \text { Reese's Stuck } \\\text { Investment } \\\text { Plan }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & \\\hline & \text { Expected } & & & { \text { Variance-Covariance Matrix } } \\\hline & \text { Return } & & & \text { Stack 1 } & \text { Stack 2 } & \text { Stack 3 } \\\hline \text { Stack 1 } & 10 \% & & \text { Stack 1 } & 0.021 & 0.018 & - 0.003 \\\hline \text { Stack 2 } & 11 \% & & \text { Stack 2 } & 0.018 & 0.070 & 0.006 \\\hline \text { Stack 3 } & 9 \% & & \text { Stack 3 } & - 0.003 & 0.006 & 0.003 \\\hline \begin{array} { l } \text { Target } \\\text { Retum }\end{array} & 10 \% & & & & & \\\hline\end{array}$$ Develop a Nonlinear Optimization Models model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.

-According to the model, what is the cross-product value for Stock 3 variance?

A) 0.00049
B) 0.00283
C) -0.00047
D) 0.00074

Question 71

LO1: Develop and solve nonlinear optimization models for different applications. Use the table below to answer the following questions).
Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.
The table below provides the relevant information. $\begin{array}{|l|l|l|l|}\hline\text { Pickson Luthiers } \\ \text { Corporation } & \text { Phone Recharging Points } & \\\hline & & & \\\hline \text { Data } & \\\hline\\\hline \text { Cell } & X \text {-coordinate } & Y \text {-coordinate } & \text { Demand } \\\hline \text { Measurements } & 2 & 5 & 27 \\\hline \text { Paint } & 1 & 3 & 12 \\\hline \text { Electricals } & 4 & 2 & 25 \\\hline\end{array}$ $$\begin{array} { | l | l | l | l | } \hline \text { Testing } & 3.5 & 5 & 5 \\\hline \text { Packnging } & 3 & 3 & 7 \\\hline & & & \\\hline \text { Maxirnum } & 4 & 5 & \\\hline\end{array}$$ The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.
Create a nonsmooth optimization model, based on the data, to answer the following questions. Hint: Choose the closest answers.)

-According to the model, which of the following is the weighted distance between the phone charger and Electricals cell?

A) 75.00
B) 125.00
C) 100.00
D) 112.50

Question 72

Use the table below to answer the following questions).
Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%. $$\begin{array} { | l | r | l | l | l | l | r | } \hline \begin{array} { l } \text { Reese's Stuck } \\\text { Investment } \\\text { Plan }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & \\\hline & \text { Expected } & & & { \text { Variance-Covariance Matrix } } \\\hline & \text { Return } & & & \text { Stack 1 } & \text { Stack 2 } & \text { Stack 3 } \\\hline \text { Stack 1 } & 10 \% & & \text { Stack 1 } & 0.021 & 0.018 & - 0.003 \\\hline \text { Stack 2 } & 11 \% & & \text { Stack 2 } & 0.018 & 0.070 & 0.006 \\\hline \text { Stack 3 } & 9 \% & & \text { Stack 3 } & - 0.003 & 0.006 & 0.003 \\\hline \begin{array} { l } \text { Target } \\\text { Retum }\end{array} & 10 \% & & & & & \\\hline\end{array}$$ Develop a Nonlinear Optimization Models model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.

-According to the model, what is the squared term value for Stock 3 variance?

A) 0.00018
B) 0.00080
C) 0.00096
D) 0.00194

Question 73

Use the table below to answer the following questions).
Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%. $$\begin{array} { | l | r | l | l | l | l | r | } \hline \begin{array} { l } \text { Reese's Stuck } \\\text { Investment } \\\text { Plan }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & \\\hline & \text { Expected } & & & { \text { Variance-Covariance Matrix } } \\\hline & \text { Return } & & & \text { Stack 1 } & \text { Stack 2 } & \text { Stack 3 } \\\hline \text { Stack 1 } & 10 \% & & \text { Stack 1 } & 0.021 & 0.018 & - 0.003 \\\hline \text { Stack 2 } & 11 \% & & \text { Stack 2 } & 0.018 & 0.070 & 0.006 \\\hline \text { Stack 3 } & 9 \% & & \text { Stack 3 } & - 0.003 & 0.006 & 0.003 \\\hline \begin{array} { l } \text { Target } \\\text { Retum }\end{array} & 10 \% & & & & & \\\hline\end{array}$$ Develop a Nonlinear Optimization Models model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.

-According to the model, what percentage of the budget should be allocated to Stock 2?

A) 90%
B) 25%
C) 50%
D) 75%

Question 74

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-According to the model, which of the following bungalows is Shirley's new accommodation closest to?

A) Bungalow 1
B) Bungalow 5
C) Bungalow 2
D) Bungalow 4

Question 75

LO1: Develop and solve nonlinear optimization models for different applications. Use the table below to answer the following questions).
Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor. The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout. The daily demand for the charging point measured as the number of trips to the charging point) at each production cell is also known. Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger. Thus, the distance from a cell to the charger is measured as rectilinear distance.
The table below provides the relevant information. $\begin{array}{|l|l|l|l|}\hline\text { Pickson Luthiers } \\ \text { Corporation } & \text { Phone Recharging Points } & \\\hline & & & \\\hline \text { Data } & \\\hline\\\hline \text { Cell } & X \text {-coordinate } & Y \text {-coordinate } & \text { Demand } \\\hline \text { Measurements } & 2 & 5 & 27 \\\hline \text { Paint } & 1 & 3 & 12 \\\hline \text { Electricals } & 4 & 2 & 25 \\\hline\end{array}$ $$\begin{array} { | l | l | l | l | } \hline \text { Testing } & 3.5 & 5 & 5 \\\hline \text { Packnging } & 3 & 3 & 7 \\\hline & & & \\\hline \text { Maxirnum } & 4 & 5 & \\\hline\end{array}$$ The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point.
Create a nonsmooth optimization model, based on the data, to answer the following questions. Hint: Choose the closest answers.)

-According to the model, which of the following is the weighted distance between the phone charger and Paint cell?

A) 36.00
B) 12.00
C) 24.00
D) 0

Question 76

Use the table below to answer the following questions).
Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. $$\begin{array} { | l | l | l | l | } \hline \text { Bungalow Location } & & & \\\hline & & & \\\hline \text { data } & & & \\\hline \text { Locatim } & \text { X-coardinate } & \text { Y-coardinate } & \text { Trips/Month } \\\hline \text { Bungaldw 1 } & 0 & 0 & 6 \\\hline \text { Bungaldw 2 } & 25 & 100 & 30 \\\hline \text { Bungaldw 3 } & 20 & 75 & 15 \\\hline \text { Bungaldw 4 } & 90 & 80 & 28 \\\hline \text { Bungaldw 5 } & 60 & 100 & 10 \\\hline\end{array}$$

-Which of the following is the ideal next step if you get the message "Solver has converged to the current solution./All constraints are satisfied," when using Solver for nonlinear optimization models?

A) Accept the values, but run Solver again from the current solution.
B) Do not accept the Solver values and re-run Solver with the starting values.
C) Accept the values and run simulations with different values.
D) Accept the values, and then tweak the values, and re-run Solver on tweaked values.

Question 77

Use the table below to answer the following questions).
Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%. $$\begin{array} { | l | r | l | l | l | l | r | } \hline \begin{array} { l } \text { Reese's Stuck } \\\text { Investment } \\\text { Plan }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & \\\hline & \text { Expected } & & & { \text { Variance-Covariance Matrix } } \\\hline & \text { Return } & & & \text { Stack 1 } & \text { Stack 2 } & \text { Stack 3 } \\\hline \text { Stack 1 } & 10 \% & & \text { Stack 1 } & 0.021 & 0.018 & - 0.003 \\\hline \text { Stack 2 } & 11 \% & & \text { Stack 2 } & 0.018 & 0.070 & 0.006 \\\hline \text { Stack 3 } & 9 \% & & \text { Stack 3 } & - 0.003 & 0.006 & 0.003 \\\hline \begin{array} { l } \text { Target } \\\text { Retum }\end{array} & 10 \% & & & & & \\\hline\end{array}$$ Develop a Nonlinear Optimization Models model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.

-According to the model, what is the squared term value for Stock 1 variance?

A) 0.00065
B) 0.00535
C) 0.01132
D) 0.00283

Question 78

Use the table below to answer the following questions).
Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%. $$\begin{array} { | l | r | l | l | l | l | r | } \hline \begin{array} { l } \text { Reese's Stuck } \\\text { Investment } \\\text { Plan }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & \\\hline & \text { Expected } & & & { \text { Variance-Covariance Matrix } } \\\hline & \text { Return } & & & \text { Stack 1 } & \text { Stack 2 } & \text { Stack 3 } \\\hline \text { Stack 1 } & 10 \% & & \text { Stack 1 } & 0.021 & 0.018 & - 0.003 \\\hline \text { Stack 2 } & 11 \% & & \text { Stack 2 } & 0.018 & 0.070 & 0.006 \\\hline \text { Stack 3 } & 9 \% & & \text { Stack 3 } & - 0.003 & 0.006 & 0.003 \\\hline \begin{array} { l } \text { Target } \\\text { Retum }\end{array} & 10 \% & & & & & \\\hline\end{array}$$ Develop a Nonlinear Optimization Models model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.

-According to the model, what is the expected total return on all stocks?

A) 18%
B) 10%
C) 11%
D) 12%

Question 79

Use the table below to answer the following questions).
Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%. $$\begin{array} { | l | r | l | l | l | l | r | } \hline \begin{array} { l } \text { Reese's Stuck } \\\text { Investment } \\\text { Plan }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & \\\hline & \text { Expected } & & & { \text { Variance-Covariance Matrix } } \\\hline & \text { Return } & & & \text { Stack 1 } & \text { Stack 2 } & \text { Stack 3 } \\\hline \text { Stack 1 } & 10 \% & & \text { Stack 1 } & 0.021 & 0.018 & - 0.003 \\\hline \text { Stack 2 } & 11 \% & & \text { Stack 2 } & 0.018 & 0.070 & 0.006 \\\hline \text { Stack 3 } & 9 \% & & \text { Stack 3 } & - 0.003 & 0.006 & 0.003 \\\hline \begin{array} { l } \text { Target } \\\text { Retum }\end{array} & 10 \% & & & & & \\\hline\end{array}$$ Develop a Nonlinear Optimization Models model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.

-According to the model, what is the squared term value for Stock 2 variance?

A) 0.00236
B) -0.00031
C) 0.00080
D) 0.00430

Question 80

Use the table below to answer the following questions).
Jonathan Reese is considering three stocks in which to invest with a fixed budget. The table below provides information on Jonathan's expected returns for each stock. The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks. He expects a total return of at least 10%. $$\begin{array} { | l | r | l | l | l | l | r | } \hline \begin{array} { l } \text { Reese's Stuck } \\\text { Investment } \\\text { Plan }\end{array} & & & & & & \\\hline & & & & & & \\\hline \text { Data } & & & & \\\hline & \text { Expected } & & & { \text { Variance-Covariance Matrix } } \\\hline & \text { Return } & & & \text { Stack 1 } & \text { Stack 2 } & \text { Stack 3 } \\\hline \text { Stack 1 } & 10 \% & & \text { Stack 1 } & 0.021 & 0.018 & - 0.003 \\\hline \text { Stack 2 } & 11 \% & & \text { Stack 2 } & 0.018 & 0.070 & 0.006 \\\hline \text { Stack 3 } & 9 \% & & \text { Stack 3 } & - 0.003 & 0.006 & 0.003 \\\hline \begin{array} { l } \text { Target } \\\text { Retum }\end{array} & 10 \% & & & & & \\\hline\end{array}$$ Develop a Nonlinear Optimization Models model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.

-According to the model, what is the expected variance of the resulting portfolio?

A) 0.014
B) 0.010
C) 0.009
D) 0.012