Question 1

In an all-integer linear program,

Accepted Answer

A) all objective function coefficients must be integer. 
B) all right-hand side values must be integer. 
C) all variables must be integer. 
D) all objective function coefficients and right-hand side values must be integer. 
A) all objective function coefficients must be integer. 
B) all right-hand side values must be integer. 
C) all variables must be integer. 
D) all objective function coefficients and right-hand side values must be integer. C

Question 2

LP relaxation refers to​

Accepted Answer

A) ​eliminating nonbinding constraints 
B) ​rounding down non-integer valued decision variables 
C) ​dropping the integer requirements for the decision variables 
D) ​accepting a non-optimal,but feasible,solution 
A) ​eliminating nonbinding constraints 
B) ​rounding down non-integer valued decision variables 
C) ​dropping the integer requirements for the decision variables 
D) ​accepting a non-optimal,but feasible,solution C

Question 3

Hansen Controls has been awarded a contract for a large number of control panels.To meet this demand,it will use its existing plants in San Diego and Houston,and consider new plants in Tulsa,St.Louis,and Portland.Finished control panels are to be shipped to Seattle,Denver,and Kansas City.Pertinent information is given in the table.
​
​
   Develop a model whose solution would reveal which plants to build and the optimal shipping schedule.

Accepted Answer

\(\begin{array} { l l } \text { Let } & P _ { i j } = \text { the number of panels shipped from source } i \text { to destination } j \ & B _ { i } = 1 \text { if plant } i \text { is built } = 0 \text { otherwise } ( i = 3,4,5 ) \ \text { Min } \quad & 350000 B _ { 3 } + 200000 B _ { 4 } + 480000 B _ { 5 } + 5 P _ { 11 } + 7 P _ { 12 } + 8 P _ { 13 } + 10 P _ { 21 } + 8 P _ { 22 } + 6 P _ { 23 } \ & + 9 P _ { 31 } + 4 P _ { 32 } + 3 P _ { 33 } + 12 P _ { 41 } + 6 P _ { 42 } + 2 P _ { 43 } + 4 P _ { 51 } + 10 P _ { 52 } + 11 P _ { 53 } \ \text { s.t. } & P _ { 11 } + P _ { 12 } + P _ { 13 } \leq 2500 \ & P _ { 21 } + P _ { 22 } + P _ { 23 } \leq 2500 \ & P _ { 31 } + P _ { 32 } + P _ { 33 } \leq 10000 B _ { 3 } \ & P _ { 41 } + P _ { 42 } + P _ { 43 } \leq 10000 B _ { 4 } \ & P _ { 51 } + P _ { 52 } + P _ { 53 } \leq 10000 B _ { 5 } \ & P _ { 11 } + P _ { 21 } + P _ { 31 } + P _ { 41 } + P _ { 51 } = 3000 \ & P _ { 12 } + P _ { 22 } + P _ { 32 } + P _ { 42 } + P _ { 52 } = 8000 \ & P _ { 13 } + P _ { 23 } + P _ { 33 } + P _ { 43 } + P _ { 53 } = 9000 \end{array}\)

Question 4

Tom's Tailoring has five idle tailors and four custom garments to make.The estimated time (in hours)it would take each tailor to make each garment is listed below.(An 'X' in the table indicates an unacceptable tailor-garment assignment. )
​​
​
   Formulate and solve an integer program for determining the tailor-garment assignments that minimize the total estimated time spent making the four garments.No tailor is to be assigned more than one garment and each garment is to be worked on by only one tailor.

Accepted Answer

Define the decision variables:x_ij = 1 if g

Question 5

If the optimal solution to the LP relaxation problem is integer,it is the optimal solution to the integer linear program.

Accepted Answer

A) True 
 B)False

Question 6

​Which of the following applications modeled in the textbook does not involve only 0 - 1 integer variables?

Accepted Answer

A) ​supply chain design 
B) ​bank location 
C) ​capital budgeting 
D) ​product design and market share optimization 
A) ​supply chain design 
B) ​bank location 
C) ​capital budgeting 
D) ​product design and market share optimization

Question 7

Kloos Industries has projected the availability of capital over each of the next three years to be $850,000,$1,000,000,and $1,200,000,respectively.It is considering four options for the disposition of the capital:
​
 (1) Research and development of a promising new product
(2) Plant exp ansi on
(3) Modernization of its current facilities
(4) Investment in a valuable piece of nearby real estate Monies not invested in these projects in a given year will NOT be available for following year's investment in the projects.The expected benefits three years hence from each of the four projects and the yearly capital outlays of the four options are summarized in the table below in $1,000,000's.
In addition,Kloos has decided to undertake exactly two of the projects,and if plant expansion is selected,it will also modernize its current facilities.
​
   Formulate and solve this problem as a binary programming problem.

Accepted Answer

None

Question 8

Let x1 ,x2 ,and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0)or are done (1).Which answer below indicates that at least two of the projects must be done?

Accepted Answer

A) x1 + x2 + x3 ≥ 2 
B) x1 + x2 + x3 ≤ 2 
C) x1 + x2 + x3 = 2 
D) x1 − x2 = 0 
A) x1 + x2 + x3 ≥ 2 
B) x1 + x2 + x3 ≤ 2 
C) x1 + x2 + x3 = 2 
D) x1 − x2 = 0

Question 9

Your express package courier company is drawing up new zones for the location of drop boxes for customers.The city has been divided into the seven zones shown below.You have targeted six possible locations for drop boxes.The list of which drop boxes could be reached easily from each zone is listed below.
Let xi = 1 if drop box location i is used,0 otherwise.Develop a model to provide the smallest number of locations yet make sure that each zone is covered by at least two boxes.
 $$\begin{array} { l l } 
\text { Zone } & \text { Can Be Served By Locations: } \
\hline \text { Downtown Financial } & 1,2,5,6 \
\text { Downtown Legal } & 2,4,5 \
\text { Retail South } & 1,2,4,6 \
\text { Retail East } & 3,4,5 \
\text { Manufacturing North } & 1,2,5 \
\text { Manufacturing East } & 3,4 \
\text { Corporate West } & 1,2,6
\end{array}$$

Accepted Answer

​
 IIin @#LAT-DLM&
s.t.
\[\begin{array} { l } 
x _

Question 10

If x1 + x2 ≤ 500y1 and y1 is 0 - 1,then if y1 is 0,x1 and x2 will be 0.

Accepted Answer

A) True 
 B)False

Question 11

Explain how integer and 0-1 variables can be used in a constraint to enable production.

Accepted Answer

Integer and 0-1 variables can be used in

Question 12

​Most practical applications of integer linear programming involve only 0 -1 integer variables.

Accepted Answer

A) True 
 B)False

Question 13

The solution to the LP Relaxation of a minimization problem will always be less than or equal to the value of the integer program minimization problem.

Accepted Answer

A) True 
 B)False

Question 14

Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs.

Accepted Answer

A) True 
 B)False

Question 15

Market Pulse Research has conducted a study for Lucas Furniture on some designs for a new commercial office desk.Three attributes were found to be most influential in determining which desk is most desirable: number of file drawers,the presence or absence of pullout writing boards,and simulated wood or solid color finish.Listed below are the part-worths for each level of each attribute provided by a sample of 7 potential Lucas customers.
​​
​
   Suppose the overall utility (sum of part-worths)of the current favorite commercial office desk is 50 for each customer.What is the product design that will maximize the share of choices for the seven sample participants? Formulate and solve,using Lindo or Excel,this 0 - 1 integer programming problem.

Accepted Answer

Define the decision variables:There are

Question 16

If Project 5 must be completed before Project 6,the constraint would be x5 − x6 ≤ 0.

Accepted Answer

A) True 
 B)False

Question 17

The constraint x1 + x2 + x3 + x4 ≤ 2 means that two out of the first four projects must be selected.

Accepted Answer

A) True 
 B)False

Question 18

Explain how integer and 0-1 variables can be used in an objective function to minimize the sum of fixed and variable
costs for production on two machines.

Accepted Answer

Integer and 0-1 variables can be used in

Question 19

The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model.

Accepted Answer

A) True 
 B)False

Question 20

Some linear programming problems have a special structure that guarantees the variables will have integer values.

Accepted Answer

A) True 
 B)False

In an all-integer linear program,

LP relaxation refers to

If the optimal solution to the LP relaxation problem is integer,it is the optimal solution to the integer linear program.

Which of the following applications modeled in the textbook does not involve only 0 - 1 integer variables?

Let x₁ ,x₂ ,and x₃ be 0 - 1 variables whose values indicate whether the projects are not done (0)or are done (1).Which answer below indicates that at least two of the projects must be done?

If x₁ + x₂ ≤ 500y₁ and y₁ is 0 - 1,then if y₁ is 0,x₁ and x₂ will be 0.

Explain how integer and 0-1 variables can be used in a constraint to enable production.

Most practical applications of integer linear programming involve only 0 -1 integer variables.

The solution to the LP Relaxation of a minimization problem will always be less than or equal to the value of the integer program minimization problem.

Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs.

If Project 5 must be completed before Project 6,the constraint would be x₅ − x₆ ≤ 0.

The constraint x₁ + x₂ + x₃ + x₄ ≤ 2 means that two out of the first four projects must be selected.

Explain how integer and 0-1 variables can be used in an objective function to minimize the sum of fixed and variable costs for production on two machines.

The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model.

Some linear programming problems have a special structure that guarantees the variables will have integer values.

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility Game Theory

Time Series Analysis Forecasting

Intro to Linear Programming

LP Sensitivity Analysis

LP Applications

Distribution Network Models

Advanced Optimization Applications

Project Scheduling

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

Exam 11: Integer Linear Programming

In an all-integer linear program,

LP relaxation refers to​

If the optimal solution to the LP relaxation problem is integer,it is the optimal solution to the integer linear program.

​Which of the following applications modeled in the textbook does not involve only 0 - 1 integer variables?

Let x1 ,x2 ,and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0)or are done (1).Which answer below indicates that at least two of the projects must be done?

If x1 + x2 ≤ 500y1 and y1 is 0 - 1,then if y1 is 0,x1 and x2 will be 0.

Explain how integer and 0-1 variables can be used in a constraint to enable production.

​Most practical applications of integer linear programming involve only 0 -1 integer variables.

The solution to the LP Relaxation of a minimization problem will always be less than or equal to the value of the integer program minimization problem.

Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs.

If Project 5 must be completed before Project 6,the constraint would be x5 − x6 ≤ 0.

The constraint x1 + x2 + x3 + x4 ≤ 2 means that two out of the first four projects must be selected.

Explain how integer and 0-1 variables can be used in an objective function to minimize the sum of fixed and variable costs for production on two machines.

The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model.

Some linear programming problems have a special structure that guarantees the variables will have integer values.

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility Game Theory

Time Series Analysis Forecasting

Intro to Linear Programming

LP Sensitivity Analysis

LP Applications

Distribution Network Models

Advanced Optimization Applications

Project Scheduling

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

LP relaxation refers to

Which of the following applications modeled in the textbook does not involve only 0 - 1 integer variables?

Let x₁ ,x₂ ,and x₃ be 0 - 1 variables whose values indicate whether the projects are not done (0)or are done (1).Which answer below indicates that at least two of the projects must be done?

If x₁ + x₂ ≤ 500y₁ and y₁ is 0 - 1,then if y₁ is 0,x₁ and x₂ will be 0.

Most practical applications of integer linear programming involve only 0 -1 integer variables.

If Project 5 must be completed before Project 6,the constraint would be x₅ − x₆ ≤ 0.

The constraint x₁ + x₂ + x₃ + x₄ ≤ 2 means that two out of the first four projects must be selected.