Question 1

Sensitivity analysis for integer linear programming

Accepted Answer

A)  can be provided only by computer. 
B)  has precisely the same interpretation as that from linear programming. 
C)  does not have the same interpretation and should be disregarded. 
D)  is most useful for 0 - 1 models. 
A)  can be provided only by computer. 
B)  has precisely the same interpretation as that from linear programming. 
C)  does not have the same interpretation and should be disregarded. 
D)  is most useful for 0 - 1 models. C

Question 2

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

Accepted Answer

A) True 
 B)False  True

Question 3

To perform sensitivity analysis involving an integer linear program, it is recommended to

Accepted Answer

A)  use the dual prices very cautiously. 
B)  make multiple computer runs. 
C)  use the same approach as you would for a linear program. 
D)  use LP relaxation. 
A)  use the dual prices very cautiously. 
B)  make multiple computer runs. 
C)  use the same approach as you would for a linear program. 
D)  use LP relaxation. B

Question 4

The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question.

Accepted Answer

A) True 
 B)False

Question 5

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 $\ge$2 
B)  x1 + x2 + x3 $\le$ 2 
C)  x1 + x2 + x3 = 2 
D)  x1 - x2 = 0 
A)  x1 + x2 + x3 $\ge$2 
B)  x1 + x2 + x3 $\le$ 2 
C)  x1 + x2 + x3 = 2 
D)  x1 - x2 = 0

Question 6

Generally, the optimal solution to an integer linear program is less sensitive to the constraint coefficients than is a linear program.

Accepted Answer

A) True 
 B)False

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:
   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

The answer of Kloos Industries has projected the availability of...

Question 8

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 9

Most practical applications of integer linear programming involve

Accepted Answer

A)  only 0-1 integer variables and not ordinary integer variables. 
B)  mostly ordinary integer variables and a small number of 0-1 integer variables. 
C)  only ordinary integer variables. 
D)  a near equal number of ordinary integer variables and 0-1 integer variables. 
A)  only 0-1 integer variables and not ordinary integer variables. 
B)  mostly ordinary integer variables and a small number of 0-1 integer variables. 
C)  only ordinary integer variables. 
D)  a near equal number of ordinary integer variables and 0-1 integer variables.

Question 10

The solution to the LP Relaxation of a maximization integer linear program provides

Accepted Answer

A)  an upper bound for the value of the objective function. 
B)  a lower bound for the value of the objective function. 
C)  an upper bound for the value of the decision variables 
D)  a lower bound for the value of the decision variables 
A)  an upper bound for the value of the objective function. 
B)  a lower bound for the value of the objective function. 
C)  an upper bound for the value of the decision variables 
D)  a lower bound for the value of the decision variables

Question 11

Slack and surplus variables are not useful in integer linear programs.

Accepted Answer

A) True 
 B)False

Question 12

Modeling a fixed cost problem as an integer linear program requires

Accepted Answer

A)  adding the fixed costs to the corresponding variable costs in the objective function. 
B)  using 0-1 variables. 
C)  using multiple-choice constraints. 
D)  using LP relaxation. 
A)  adding the fixed costs to the corresponding variable costs in the objective function. 
B)  using 0-1 variables. 
C)  using multiple-choice constraints. 
D)  using LP relaxation.

Question 13

Rounding the solution of an LP Relaxation to the nearest integer values provides

Accepted Answer

A)  a feasible but not necessarily optimal integer solution. 
B)  an integer solution that is optimal. 
C)  an integer solution that might be neither feasible nor optimal. 
D)  an infeasible solution. 
A)  a feasible but not necessarily optimal integer solution. 
B)  an integer solution that is optimal. 
C)  an integer solution that might be neither feasible nor optimal. 
D)  an infeasible solution.

Question 14

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

The answer of Hansen Controls has been awarded a contract...

Question 15

The classic assignment problem can be modeled as a 0-1 integer program.

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

A) True 
 B)False

Question 17

Multiple choice constraints involve binary variables.

Accepted Answer

A) True 
 B)False

Question 18

In general, rounding large values of decision variables to the nearest integer value causes fewer problems than rounding small values.

Accepted Answer

A) True 
 B)False

Question 19

A multiple choice constraint involves selecting k out of n alternatives, where k $\ge$ 2.

Accepted Answer

A) True 
 B)False

Question 20

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.

Accepted Answer

Sensitivity analysis for integer linear programming

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

To perform sensitivity analysis involving an integer linear program, it is recommended to

The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question.

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?

Generally, the optimal solution to an integer linear program is less sensitive to the constraint coefficients than is a linear program.

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

Most practical applications of integer linear programming involve

The solution to the LP Relaxation of a maximization integer linear program provides

Slack and surplus variables are not useful in integer linear programs.

Modeling a fixed cost problem as an integer linear program requires

Rounding the solution of an LP Relaxation to the nearest integer values provides

The classic assignment problem can be modeled as a 0-1 integer program.

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

Multiple choice constraints involve binary variables.

In general, rounding large values of decision variables to the nearest integer value causes fewer problems than rounding small values.

A multiple choice constraint involves selecting k out of n alternatives, where k $\ge$ 2.

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

Filters

Exam 7: Integer Linear Programming

Sensitivity analysis for integer linear programming

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

To perform sensitivity analysis involving an integer linear program, it is recommended to

The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question.

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?

Generally, the optimal solution to an integer linear program is less sensitive to the constraint coefficients than is a linear program.

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

Most practical applications of integer linear programming involve

The solution to the LP Relaxation of a maximization integer linear program provides

Slack and surplus variables are not useful in integer linear programs.

Modeling a fixed cost problem as an integer linear program requires

Rounding the solution of an LP Relaxation to the nearest integer values provides

The classic assignment problem can be modeled as a 0-1 integer program.

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

Multiple choice constraints involve binary variables.

In general, rounding large values of decision variables to the nearest integer value causes fewer problems than rounding small values.

A multiple choice constraint involves selecting k out of n alternatives, where k ≥\ge≥ 2.

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

Filters

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 $\le$ 500y₁ and y₁ is 0 - 1, then if y₁ is 0, x₁ and x₂ will be 0.

A multiple choice constraint involves selecting k out of n alternatives, where k $\ge$ 2.