Deck 14: Integer, nonlinear, and Advanced Optimization Methods

Question 1

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
Determine the objective function.

A)Maximize 1,000X₁ + 1,430X₂ + 1,260X₃
B)Minimize 3X₁ + 8X₂ + 2X₃ + 11X₄ + 7X₅ + 5X₆
C)Minimize 3X₂ + 4X₃ + 2X₅
D)Maximize 1X₁ + 8X₂ + 2X₃ + 6X₄ + 3X₅ + 4X₆

Answer 1

Minimize 3X₁ + 8X₂ + 2X₃ + 11X₄ + 7X₅ + 5X₆

Question 2

A mixed integer linear optimization model differs from a nonlinear optimization model in that the mixed integer linear optimization model ________.

A)contains terms that cannot be written as constant times a variable
B)is considerably more difficult to solve than the nonlinear optimization model
C)uses equalities and inequalities to describe constraints in the business decision problem
D)contains only a subset of variables that are restricted to being integers while others are continuous

Answer 2

contains only a subset of variables that are restricted to being integers while others are continuous

Question 3

A nonlinear optimization model differs from a mixed integer linear optimization model in that the nonlinear optimization model ________.

A)contains terms that cannot be written as constant times a variable
B)is considerably more easy to solve than the mixed integer linear optimization model
C)uses equalities and nonequalities to describe constraints in the business decision problem
D)contains only a subset of variables that are restricted to being integers while others are continuous

Answer 3

contains terms that cannot be written as constant times a variable

Question 4

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
The constraint for 16-inch rolls is formulated as ________.

A)7X₁ + 2X₂ + 2X₅ + 2X₆ ≥ 1,430
B)2X₂ + 6X₃ + 5X₄ ≥ 715
C)3X₂ + 4X₃ + 2X₅ ≤ 1,430
D)X₁ + X₂ + X₅ + X₆ ≤ 715

Question 5

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
Using Solver,the minimum value of the objective function is ________.

A)1,260 units
B)1,718 units
C)1,430 units
D)1,000 units

Question 6

Use the data shown below to answer the following question(s).
Malone Inc.has identified five potential new processes; however,the firm is constrained by its available budget and human resources.Each process is expected to generate a return (given by the net present value)but requires a fixed amount of cash and personnel.Because the resources are limited,all processes cannot be selected.Processes cannot be partially completed; thus,either the process must be undertaken completely or not at all.The data are given in the table below.If a process is selected,it generates the full value of the expected return and requires the full amount of cash and personnel shown in the table.Define X_i = 1 if process i is selected,and 0 otherwise.
Determine the expression that explains the personnel limitation.

A)5X₁ + 3X₂ + 3X₃ + 5X₄ + 2X₅ ≥ 12
B)5X₁+ 3X₂ + 3X₅ ≥ 12
C)5X₁+ 3X₂ + 3X₅ ≤ 12
D)5X₁ + 3X₂ + 2X₃ + 5X₄ + 3X₅ ≤ 12

Question 7

Use the data shown below to answer the following question(s).
Malone Inc.has identified five potential new processes; however,the firm is constrained by its available budget and human resources.Each process is expected to generate a return (given by the net present value)but requires a fixed amount of cash and personnel.Because the resources are limited,all processes cannot be selected.Processes cannot be partially completed; thus,either the process must be undertaken completely or not at all.The data are given in the table below.If a process is selected,it generates the full value of the expected return and requires the full amount of cash and personnel shown in the table.Define X_i = 1 if process i is selected,and 0 otherwise.
Using Solver,identify the combination of the processes that are selected.

A)Process 2,Process 3,and Process 4
B)Process 3 and Process 4
C)Process 1,Process 2,and Process 5
D)Process 1,Process 4,and Process 5

Question 8

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
What is the number of 25-inch rolls produced?

A)1,264 units
B)1,718 units
C)1,432 units
D)1,000 units

Question 9

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
If we are to use Solver to generate the optimal solution,determine the number of 115-inch rolls produced using the cutting pattern 1.

A)172 units
B)1,264 units
C)316 units
D)0 units

Question 10

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
Determine the constraint modeled for 25-inch rolls.

A)3X₁ + 8X₂ + 2X₃ + 11X₄ + 7X₅ + 5X₆ ≥ 1,260
B)X₂ + 2X₃ + X₄ ≥ 630
C)3X₂ + 4X₃ + 2X₅ ≥ 1,260
D)7X₂ + X₃ ≤ 630

Question 11

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
If the demand for the 25-inch rolls increases to 1,300,the total scrap value ________.

A)increases by 40 units
B)does not show an increase or a decrease
C)increases by 13 units
D)decreases by 6 units

Question 12

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
If we are to use Solver to generate the optimal solution,identify the number of 115-inch rolls produced using the cutting pattern 3.

A)172 units
B)316 units
C)114 units
D)0 units

Question 13

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
What is the number of 13-inch rolls produced?

A)1,264 units
B)1,718 units
C)1,432 units
D)1,000 units

Question 14

Use the data shown below to answer the following question(s).
Malone Inc.has identified five potential new processes; however,the firm is constrained by its available budget and human resources.Each process is expected to generate a return (given by the net present value)but requires a fixed amount of cash and personnel.Because the resources are limited,all processes cannot be selected.Processes cannot be partially completed; thus,either the process must be undertaken completely or not at all.The data are given in the table below.If a process is selected,it generates the full value of the expected return and requires the full amount of cash and personnel shown in the table.Define X_i = 1 if process i is selected,and 0 otherwise.
What is the objective function?

A)Maximize $27,500X₁ + $41,500X₂ + $27,500X₃ + $70,000 X₄ + $70,000 X₅
B)Maximize $5,000X₁ + $3,000X₂ + $2,000 X₃ + $5,000 X₄ + $3,000 X₅
C)Maximize $90,000X₁ + $110,000X₂ + $75,000 X₃ + $70,000 X₄ + $100,000 X₅
D)Maximize $180,000X₁ + $220,000X₂ + $150,000X₃ + $140,000X₄ + $200,000X₅

Question 15

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
Identify the constraint specified for 13-inch rolls.

A)7X₂ ≤ 1,000
B)2X₂ + 6X₄ + 2X₅ + 7X₆ ≥ 1,430
C)X₃ + 8X₄ + 2X₅ + 6X₆ ≥ 1,000
D)X₂ + 4X₄ + X₅ + 3X₆ ≤ 500

Question 16

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
Using Solver,determine the number of 115-inch rolls produced with the cutting pattern 6.

A)172 units
B)316 units
C)114 units
D)0 units

Question 17

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
Integer models are discontinuous by their very nature.Hence,________.

A)no Answer report is provided by Solver
B)no Sensitivity report is provided by Solver
C)a single limit report is provided by Solver
D)two limit reports are provided by Solver

Question 18

Integer linear optimization models differ from nonlinear optimization models in that integer linear optimization models ________.

A)contain some or all variables that are restricted to being whole numbers
B)use only inequalities to describe the constraints
C)use only equalities to describe the constraints
D)contain terms that cannot be written as constant times a variable

Question 19

Use the scenario below to answer the following question(s).
A company makes standard 115-inch-wide rolls of thin sheet metal,and slits them into smaller rolls to meet customer orders for widths of 13,16,and 25 inches.The demands for these widths vary from week to week.From a 115-inch roll,there are many different ways to slit 13-,16-,and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock.Of course,one would want to use as much of the roll as possible to avoid costly scrap.For example,one could cut seven 16-inch rolls,leaving a 3-inch piece of scrap.Finding good cutting patterns for a large set of end products is in itself a challenging problem.Suppose that the company has proposed the following cutting patterns: Demands this week are 1,000 13-inch rolls,1,430 16-inch rolls,and 1,260 25-inch rolls.The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define X_i to be the number of 115-inch rolls to cut using cutting pattern i,for i = 1,…,6.
Note that X_i needs to be a whole number because each roll that is cut generates a different number of end items.
What is the number of 16-inch rolls produced?

A)1,264 units
B)1,718 units
C)1,432 units
D)1,000 units

Question 20

Use the data shown below to answer the following question(s).
Malone Inc.has identified five potential new processes; however,the firm is constrained by its available budget and human resources.Each process is expected to generate a return (given by the net present value)but requires a fixed amount of cash and personnel.Because the resources are limited,all processes cannot be selected.Processes cannot be partially completed; thus,either the process must be undertaken completely or not at all.The data are given in the table below.If a process is selected,it generates the full value of the expected return and requires the full amount of cash and personnel shown in the table.Define X_i = 1 if process i is selected,and 0 otherwise.
Identify the expression that explains the cash limitation.

A)$27,500X₁ + $41,500X₂ + $12,000X₃ + $24,500X₄ + $61,000X₅ ≤ $150,000
B)$90,000X₁ + $110,000X₂ + $75,000X₃ + $70,000X₄ + $100,000X₅ ≤ $150,000
C)$27,500X₁ + $41,500X₂ + $12,000X₃ + $24,500X₄ + $61,000X₅ ≥ $150,000
D)$90,000X₁ + $110,000X₂ + $75,000X₃ + $70,000X₄ + $100,000X₅ ≥ $150,000

Question 21

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Using Solver,determine the amount to be shipped from the plant in Orlando to the distribution center in Minnesota.

A)600 units
B)0 units
C)200 units
D)1,000 units

Question 22

Use the data shown below to answer the following question(s).
Malone Inc.has identified five potential new processes; however,the firm is constrained by its available budget and human resources.Each process is expected to generate a return (given by the net present value)but requires a fixed amount of cash and personnel.Because the resources are limited,all processes cannot be selected.Processes cannot be partially completed; thus,either the process must be undertaken completely or not at all.The data are given in the table below.If a process is selected,it generates the full value of the expected return and requires the full amount of cash and personnel shown in the table.Define X_i = 1 if process i is selected,and 0 otherwise.
Using Solver,the total return for the optimal solution is ________.

A)$300,000
B)$245,000
C)$170,000
D)$445,000

Question 23

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Which of the following is the capacity constraint that is related to the Baltimore plant?

A)X₁₁ + X₁₂ + X₁₃ + X₁₄ ≤ 4,000
B)X₁₁ + X₁₂ + X₁₃ + X₁₄ ≤ 2,400
C)X₁₁ + X₁₂ + X₁₃ + X₁₄ ≤ 3,000Y₁
D)X₁₁ + X₁₂ + X₁₃ + X₁₄ ≥ 3,000Y₂

Question 24

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
The demand constraint for Dallas is ________.

A)X₂₁ + X₂₂ + X₂₃ + X₂₄ ≤ 1,000
B)X₁₂ + X₂₂ + X₃₂ + X₄₂ = 1,000
C)X₂₁ + X₂₂ + X₂₃ + X₂₄ = 1,000
D)X₁₂ + X₂₂ ≥ 1,000

Question 25

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
The inequality/equality that explains the demand constraint for Minnesota is ________.

A)X₁₁ + X₁₂ + X₁₃ + X₁₄ ≤ 600
B)X₁₁ + X₁₂ + X₁₃ + X₁₄ = 600
C)X₁₁ + X₂₁ + X₃₁ + X₄₁ = 600
D)X₁₁ + X₂₁ ≥ 600

Question 26

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Which of the following is the capacity constraint that is related to the Ohio plant?

A)X₃₁ + X₃₂ + X₃₃ + X₃₄ ≥ 3,000Y₂
B)X₃₁ + X₃₂ + X₃₃ + X₃₄ ≤ 3,600
C)X₃₁ + X₃₂ + X₃₃ + X₃₄ ≤ 1,400
D)X₃₁ + X₃₂ + X₃₃ + X₃₄ ≤ 3,000Y₁

Question 27

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Determine the objective function.

A)Minimize 25.20X₁₁ + 28.70X₁₂ + 23.04X₁₃ + 35.16X₁₄ + 19.50X₂₁ + 32.52X₂₂ + 16.22X₂₃ + 35.84X₂₄
B)Maximize 25.20X₁₁ + 28.70X₁₂ + 23.04X₁₃ + 35.16X₁₄ + 19.50X₂₁ + 32.52X₂₂ + 16.22X₂₃ + 35.84X₂₄
C)Minimize 25.20X₁₁ + 28.70X₁₂ + 23.04X₁₃ + 35.16X₁₄ + 19.50X₂₁ + 32.52X₂₂ + 16.22X₂₃ + 35.84X₂₄ + 20.82X₃₁ + 23.08X₃₂ + 19.74X₃₃ + 23.28X₃₄ + 27.76X₄₁ + 33.90X₄₂ + 25.02X₄₃ + 16.36X₄₄
D)Maximize 25.20X₁₁ + 28.70X₁₂ + 23.04X₁₃ + 35.16X₁₄ + 19.50X₂₁ + 32.52X₂₂ + 16.22X₂₃ + 35.84X₂₄ + 20.82X₃₁ + 23.08X₃₂ + 19.74X₃₃ + 23.28X₃₄ + 27.76X₄₁ + 33.90X₄₂ + 25.02X₄₃ + 16.36X₄₄

Question 28

Use the data shown below to answer the following question(s).
Malone Inc.has identified five potential new processes; however,the firm is constrained by its available budget and human resources.Each process is expected to generate a return (given by the net present value)but requires a fixed amount of cash and personnel.Because the resources are limited,all processes cannot be selected.Processes cannot be partially completed; thus,either the process must be undertaken completely or not at all.The data are given in the table below.If a process is selected,it generates the full value of the expected return and requires the full amount of cash and personnel shown in the table.Define X_i = 1 if process i is selected,and 0 otherwise.
Using Solver,determine the total number of personnel used.

A)28
B)10
C)18
D)11

Question 29

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
If we are to use Solver to determine where the new plant has to be built,what is the amount shipped from Ohio to Los Angeles?

A)0 units
B)400 units
C)1,000 units
D)3,000 units

Question 30

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Using Solver,determine the amount to be shipped from the plant in Orlando to the distribution center in Los Angeles.

A)600 units
B)1,400 units
C)200 units
D)3,000 units

Question 31

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Using Solver,determine the amount to be shipped from the plant in Baltimore to the distribution center in Dallas.

A)0 units
B)400 units
C)1,400 units
D)1,000 units

Question 32

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Using Solver,determine the amount to be shipped from the plant in Baltimore to the distribution center in Minnesota.

A)0 units
B)400 units
C)200 units
D)1,000 units

Question 33

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
The demand constraint for Los Angeles is ________.

A)X₃₁ + X₃₂ + X₃₃ + X₃₄ = 1,400
B)X₁₃ + X₂₃ + X₃₃ + X₄₃ = 1,400
C)X₁₃ + X₂₃ + X₃₃ + X₄₃ ≥ 1,400
D)X₃₁ + X₃₂ ≤ 1,400

Question 34

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Which of the following explains the capacity constraint for the Kansas plant?

A)X₄₁ + X₄₂ + X₄₃ + X₄₄ ≤ 3,000Y₁
B)X₄₁ + X₄₂ + X₄₃ + X₄₄ ≤ 3,000Y₂
C)X₄₁ + X₄₂ + X₄₃ + X₄₄ ≤ 3,600
D)X₄₁ + X₄₂ + X₄₃ + X₄₄ ≤ 1,400

Question 35

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Which of the following is the capacity constraint for the Orlando plant?

A)X₂₁ + X₂₂ + X₂₃ + X₂₄ ≤ 1,600
B)X₂₁ + X₂₂ + X₂₃ + X₂₄ ≤ 2,400
C)X₂₁ + X₂₂ + X₂₃ + X₂₄ ≤ 3,000Y₁
D)X₂₁ + X₂₂ + X₂₃ + X₂₄ ≥ 3,000Y₂

Question 36

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
The inequality/equality that explains the demand constraint for Memphis is ________.

A)X₄₁ + X₄₂ ≤ 1,400
B)X₄₁ + X₄₂+ X₄₃ + X₄₄ = 3,600
C)X₁₄ + X₂₄+ X₃₄ + X₄₄ ≥ 1,400
D)X₁₄ + X₂₄+ X₃₄ + X₄₄ = 3,600

Question 37

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Using Solver,determine the amount to be shipped from the plant in Baltimore to the distribution center in Memphis.

A)0 units
B)400 units
C)600 units
D)1,000 units

Question 38

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
To guarantee that only one new plant is built,we must have the constraint ________.

A)Y₁ > 1
B)Y₁ + Y₂ ≤ 1
C)Y₁ + Y₂ = 1
D)Y₁ + Y₂ ≥ 1

Question 39

Use the data shown below to answer the following question(s).
Malone Inc.has identified five potential new processes; however,the firm is constrained by its available budget and human resources.Each process is expected to generate a return (given by the net present value)but requires a fixed amount of cash and personnel.Because the resources are limited,all processes cannot be selected.Processes cannot be partially completed; thus,either the process must be undertaken completely or not at all.The data are given in the table below.If a process is selected,it generates the full value of the expected return and requires the full amount of cash and personnel shown in the table.Define X_i = 1 if process i is selected,and 0 otherwise.
Using Solver,identify the processes that are rejected.

A)Process 2 and Process 5
B)Process 3 and Process 4
C)Process 1 and Process 2
D)Process 1,Process 2,and Process 5

Question 40

Use the data shown below to answer the following question(s).
Malone Inc.has identified five potential new processes; however,the firm is constrained by its available budget and human resources.Each process is expected to generate a return (given by the net present value)but requires a fixed amount of cash and personnel.Because the resources are limited,all processes cannot be selected.Processes cannot be partially completed; thus,either the process must be undertaken completely or not at all.The data are given in the table below.If a process is selected,it generates the full value of the expected return and requires the full amount of cash and personnel shown in the table.Define X_i = 1 if process i is selected,and 0 otherwise.
Using Solver,determine the total cash used for the optimal solution.

A)$120,000
B)$300,000
C)$130,000
D)$600,000

Question 41

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
What is the new price of a single gold suite,using Solver?

A)$98.00
B)$79.81
C)$90.00
D)$147.98

Question 42

Use the data shown below to answer the following question(s).
Hudson's Creators is a company that produces embroidered clothes.Forecasts of sales for the next year are 200 in the autumn,450 in the winter,and 100 in the spring.Plain clothes are purchased from a supplier for $25.The cost of capital is estimated to be 28% per year (or 7% per quarter); thus,the holding cost per item is 0.07($25)= $1.75 per quarter.Hudson hires art students part-time to produce his designs during the autumn,and they earn $6.50 per hour.Because of the high demand for part-time help during the winter holiday season,labor rates are higher in the winter,and workers earn $8.00 per hour.In the spring,labor is more difficult to keep,and the owner must pay $7.25 per hour to retain qualified help.Each embroidered cloth takes 2 hours to complete.Define the model based on how the production should be planned over the three quarters to minimize the combined production and inventory holding costs.
Use the following terms to define the decision variables:
P_A = amount to produce in autumn
P_W = amount to produce in winter
P_S = amount to produce in spring
I_A = inventory held at the end of autumn
I_W = inventory held at the end of winter
I_S = inventory held at the end of spring
Suppose that Hudson must rent some equipment to produce his products,which costs $75 for three months.The equipment can be rented or returned each quarter,so if nothing is produced in a quarter,it makes no sense to incur the rental cost.
The fixed costs can be incorporated into the model by defining an additional set of variables:
Y_A = 1 if production occurs during the autumn,and 0 if not
Y_W = 1 if production occurs during the winter,and 0 if not
Y_S = 1 if production occurs during the spring,and 0 if not
Which of the following is the basic material balance equation for the spring season?

A)P_S + I_S ≤ 100
B)P_S - I_S ≥ 200
C)P_S + I_W - I_S = 100
D)P_S + I_S - I_W = 450

Question 43

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Using Solver,determine the optimal cost involved in shipping cars from Kansas to Memphis.

A)$48,090
B)$84,009
C)$49,080
D)$98,004

Question 44

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
The constraint that models the stated price range of a platinum suite is ________.

A)60 ≤ = P ≤ 79.5
B)120 ≤ P ≤ 149
C)120P² - 149P ≥ 0
D)60P² - 79.5P ≤ 0

Question 45

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
The constraint that models the stated price range of a standard suite is ________.

A)70 ≤ S ≤ 90
B)90S² - 70S ≥ 0
C)70S² - 90S ≤ 0
D)35 ≤ S ≤ 45

Question 46

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
The projected number of total suites sold or the total suite capacity is modeled by the constraint ________.

A)1,755 + 6.176471S + 4.081633G + 1.079137P ≥ 755
B)6.176471 + 1,730.755S + 1.079137G + 4.081633P ≥ 755
C)1,775 - 6.176471S - 4.081633G - 1.079137P ≤ 755
D)1.079137 - 6.176471S - 4.081633G - 1,730.755 P ≤ 755

Question 47

Use the data shown below to answer the following question(s).
Hudson's Creators is a company that produces embroidered clothes.Forecasts of sales for the next year are 200 in the autumn,450 in the winter,and 100 in the spring.Plain clothes are purchased from a supplier for $25.The cost of capital is estimated to be 28% per year (or 7% per quarter); thus,the holding cost per item is 0.07($25)= $1.75 per quarter.Hudson hires art students part-time to produce his designs during the autumn,and they earn $6.50 per hour.Because of the high demand for part-time help during the winter holiday season,labor rates are higher in the winter,and workers earn $8.00 per hour.In the spring,labor is more difficult to keep,and the owner must pay $7.25 per hour to retain qualified help.Each embroidered cloth takes 2 hours to complete.Define the model based on how the production should be planned over the three quarters to minimize the combined production and inventory holding costs.
Use the following terms to define the decision variables:
P_A = amount to produce in autumn
P_W = amount to produce in winter
P_S = amount to produce in spring
I_A = inventory held at the end of autumn
I_W = inventory held at the end of winter
I_S = inventory held at the end of spring
Suppose that Hudson must rent some equipment to produce his products,which costs $75 for three months.The equipment can be rented or returned each quarter,so if nothing is produced in a quarter,it makes no sense to incur the rental cost.
The fixed costs can be incorporated into the model by defining an additional set of variables:
Y_A = 1 if production occurs during the autumn,and 0 if not
Y_W = 1 if production occurs during the winter,and 0 if not
Y_S = 1 if production occurs during the spring,and 0 if not
Which of the following is the basic material balance equation for the autumn season?

A)P_A + I_A - I_W = 200
B)P_A + I_A ≥ 100
C)P_A - I_A = 200
D)P_W + I_A - I_W = 450

Question 48

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
Which of the following is the objective function?

A)Maximize 875S² + 600G² + 255.7554P² - 6.176471S - 4.081633G - 1.079137P
B)Maximize 875S + 600G + 300P - 6.176471S² - 4.081633G² - 1.079137P²
C)Maximize -875S² - 600G² - 300P² + 6.176471S + 4.081633G + 1.079137P
D)Maximize 600S + 255.7554G + 875P - 4.081633S² - 4.081633G² - 6.176471P²

Question 49

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
The constraint that models the stated price range of a gold suite is ________.

A)45 ≤ G ≤ 55
B)45G² - 55G ≥ 0
C)90G² - 110G ≤ 0
D)90 ≤ G ≤ 110

Question 50

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Using Solver,determine the optimal cost involved in shipping cars from Baltimore to Minnesota.

A)$8,010
B)$10,080
C)$1,080
D)$80,100

Question 51

Use the data shown below to answer the following question(s).
Hudson's Creators is a company that produces embroidered clothes.Forecasts of sales for the next year are 200 in the autumn,450 in the winter,and 100 in the spring.Plain clothes are purchased from a supplier for $25.The cost of capital is estimated to be 28% per year (or 7% per quarter); thus,the holding cost per item is 0.07($25)= $1.75 per quarter.Hudson hires art students part-time to produce his designs during the autumn,and they earn $6.50 per hour.Because of the high demand for part-time help during the winter holiday season,labor rates are higher in the winter,and workers earn $8.00 per hour.In the spring,labor is more difficult to keep,and the owner must pay $7.25 per hour to retain qualified help.Each embroidered cloth takes 2 hours to complete.Define the model based on how the production should be planned over the three quarters to minimize the combined production and inventory holding costs.
Use the following terms to define the decision variables:
P_A = amount to produce in autumn
P_W = amount to produce in winter
P_S = amount to produce in spring
I_A = inventory held at the end of autumn
I_W = inventory held at the end of winter
I_S = inventory held at the end of spring
Suppose that Hudson must rent some equipment to produce his products,which costs $75 for three months.The equipment can be rented or returned each quarter,so if nothing is produced in a quarter,it makes no sense to incur the rental cost.
The fixed costs can be incorporated into the model by defining an additional set of variables:
Y_A = 1 if production occurs during the autumn,and 0 if not
Y_W = 1 if production occurs during the winter,and 0 if not
Y_S = 1 if production occurs during the spring,and 0 if not
Which of the following is the basic material balance equation for the winter season?

A)P_W + I_W = 100
B)P_W - I_W ≥ 450
C)P_W + I_A - I_W ≤ 100
D)P_W + I_A - I_W = 450

Question 52

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Using Solver,determine the optimal cost involved in shipping cars from Baltimore to Memphis.

A)$21,069
B)$12,096
C)$12,029
D)$21,096

Question 53

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Using Solver,determine the optimal cost involved in shipping cars from Orlando to Los Angeles.

A)$7,082
B)$80,702
C)$70,802
D)$22,708

Question 54

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
Which of the following is the expression that can be used to determine the projected number of standard suites sold?

A)875 - 6.176471S
B)600 - 4.081633S
C)255.7554 - 1.079137S
D)255.7554 + 1.079137S

Question 55

Use the data shown below to answer the following question(s).
Hudson's Creators is a company that produces embroidered clothes.Forecasts of sales for the next year are 200 in the autumn,450 in the winter,and 100 in the spring.Plain clothes are purchased from a supplier for $25.The cost of capital is estimated to be 28% per year (or 7% per quarter); thus,the holding cost per item is 0.07($25)= $1.75 per quarter.Hudson hires art students part-time to produce his designs during the autumn,and they earn $6.50 per hour.Because of the high demand for part-time help during the winter holiday season,labor rates are higher in the winter,and workers earn $8.00 per hour.In the spring,labor is more difficult to keep,and the owner must pay $7.25 per hour to retain qualified help.Each embroidered cloth takes 2 hours to complete.Define the model based on how the production should be planned over the three quarters to minimize the combined production and inventory holding costs.
Use the following terms to define the decision variables:
P_A = amount to produce in autumn
P_W = amount to produce in winter
P_S = amount to produce in spring
I_A = inventory held at the end of autumn
I_W = inventory held at the end of winter
I_S = inventory held at the end of spring
Suppose that Hudson must rent some equipment to produce his products,which costs $75 for three months.The equipment can be rented or returned each quarter,so if nothing is produced in a quarter,it makes no sense to incur the rental cost.
The fixed costs can be incorporated into the model by defining an additional set of variables:
Y_A = 1 if production occurs during the autumn,and 0 if not
Y_W = 1 if production occurs during the winter,and 0 if not
Y_S = 1 if production occurs during the spring,and 0 if not
Which of the following is the objective function?

A)Minimize 13P_A + 16P_W + 14.50P_S + 75(I_A + I_W + I_S)+ 1.75 (Y_A + Y_W + Y_S)
B)Minimize 13P_A + 14.50P_W + 16P_S + 75(I_A + I_W + I_S)+ 1.75 (Y_A + Y_W + Y_S)
C)Minimize 13P_A + 16P_W + 14.50P_S + 1.75 (I_A + I_W + I_S)+ 75(Y_A + Y_W + Y_S)
D)Minimize 14.50P_A + 13P_W + 16P_S + 1.75(I_A + I_W + I_S)+ 75(Y_A + Y_W + Y_S)

Question 56

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
Which of the following is the expression that can be used to determine the projected number of platinum suites sold?

A)875 - 6.176471P
B)255.7554 - 1.079137P
C)600 - 4.081633P
D)300 - 1.079137P

Question 57

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
Using Solver,determine the new price of a single standard suite.

A)$85.00
B)$79.81
C)$90.00
D)$147.98

Question 58

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
Using Solver,determine the total optimal cost.

A)$104,356
B)$121,596
C)$135,564
D)$110,348

Question 59

Use the case below to answer the following question(s).
Rolling Inc.produces cars at two plants: Baltimore,Maryland,and Orlando,Florida.They ship them to major distribution centers in Minnesota,Dallas,Los Angeles,and Memphis.The Accounting,Production,and Marketing departments have provided the information in the table below,which shows the unit cost of shipping between any plant and distribution center to minimize the total transportation cost,not exceed available capacity,and meet customer demand. Suppose demand forecasts exceed the existing capacity and the company is considering adding a new plant from among two choices: Ohio or Kansas.Both plants would have a capacity of 3,000 units but only one can be built.The table below shows the revised data. Use double-subscripted variables to simplify the formulation.Define X_ij = amount shipped from plant i to distribution center j,where i = 1 represents Baltimore,and j = 1 represents Minnesota.
Define a binary variable for the decision of which plant to build: Y₁ = 1 if the Ohio plant is built,and Y₂ = 1 if the Kansas plant is built.
If we are to use Solver to determine where the new plant has to be built,what is the amount shipped from Kansas to Memphis?

A)0 units
B)3,000 units
C)200 units
D)1,000 units

Question 60

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
Which of the following is the expression that can be used to determine the projected number of gold suites sold?

A)875 - 6.176471G
B)200 - 4.081633G
C)600 - 4.081633G
D)255.7554 - 1.079137G

Question 61

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
Determine the projected revenue for selling the projected number of gold suites.

A)$20,938.78
B)$20,762.98
C)$30,491.55
D)$72,193.31

Question 62

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
Determine the Lagrange multiplier.

A)80.34
B)90.34
C)17.96
D)5.17

Question 63

In a nonlinear optimization model,the terms cannot be written as a constant times a variable.

Question 64

A(n)________ is a forecast statistic that is restricted to fall within a specified lower and upper bound.

A)objective
B)requirement
C)decision variable
D)permutation

Question 65

Solver's ________ algorithm uses an approach that remembers the best solutions it finds,and then modifies or combines them in attempting to find better solutions.

A)Standard LP/Quadratic
B)Standard GRG Linear
C)Standard Evolutionary
D)Standard GRG Nonlinear

Question 66

Sensitivity information for integer models can be generated in the same manner as for linear models.

Question 67

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
Determine the projected revenue for selling the projected number of standard suites.

A)$20,938.78
B)$20,762.98
C)$30,491.55
D)$72,193.31

Question 68

Nonlinear optimization models are considerably easier to solve than linear or integer models.

Question 69

The inherent risks that exist in optimization models can be better understood and mitigated using the capabilities of risk analysis software such as ________.

A)Solver
B)PHStat
C)Crystal Ball
D)MS Excel

Question 70

In the sensitivity report for nonlinear optimization models,the ________ is analogous to the shadow price in linear optimization sensitivity reports.

A)Final value
B)Reduced gradient
C)Lagrange multiplier
D)Lower limit

Question 71

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
Determine the projected revenue for selling the projected number of platinum suites.

A)$20,938.78
B)$20,762.98
C)$30,491.55
D)$72,193.31

Question 72

In the Adjustable Cells section of a nonlinear optimization Solver report,the Reduced Gradient is analogous to the Reduced Cost in linear models.

Question 73

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
Determine the projected revenue for selling the projected number of total suites.

A)$20,938.78
B)$20,762.98
C)$30,491.55
D)$72,193.31

Question 74

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
Using Solver,determine the projected number of standard suites sold.

A)382
B)233
C)140
D)755

Question 75

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
The projected number of platinum suites sold is ________.

A)382
B)233
C)140
D)755

Question 76

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
The projected number of gold suites sold is ________.

A)382
B)233
C)140
D)755

Question 77

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
If the number of available suites increases by 1 to 756,using the Lagrange multiplier,the total revenue would ________.

A)increase by approximately $55.76
B)decrease by approximately $17.96
C)decrease by approximately $2,100.76
D)increase by approximately $17.96

Question 78

Integer models are continuous by their very nature.

Question 79

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
What is the new price of a single platinum suite,using Solver?

A)$139.00
B)$79.81
C)$90.00
D)$147.98

Question 80

Use the case below to answer the following question(s).
The Tipton Hotel is considering a major remodeling effort and needs to determine the best combination of rates and suite sizes to maximize revenues.Currently,the hotel has 755 suites with the following history: Each market segment has its own price/demand elasticity.Estimates are: This means,for example,that a 1% decrease in the price of a standard suite will increase the number of suites sold by 1.5%.Similarly,a 1% increase in the price will decrease the number of suites sold by 1.5%.For any pricing structure (in $),the projected number of suites of a given type sold (we will allow continuous values for this problem)can be found using the formula:
(Historical average number of suites sold)+ (Elasticity)(New price - Current price)(Historical average number of suites sold)/(Current price)
The hotel owners want to keep the price of a standard suite between $70 and $90; a gold suite between $90 and $110; and a platinum suite between $120 and $149.
Define S = price of a standard suite,G = price of a gold suite,and P = price of a platinum suite.
If the number of available suites increases by 1 to 756,re-solving the model using Solver,the total revenue would ________.

A)decrease by approximately $55.76
B)increase by approximately $17.82
C)decrease by approximately $2,100.76
D)increase by approximately $17.96