Question 1

A requirement that two 0-1 variables both be either in or out of a solution together is a​

Accepted Answer

A) ​k out of n alternatives constraint 
B) ​conditional constraint 
C) ​mutually exclusive constraint 
D) ​corequisite constraint 
A) ​k out of n alternatives constraint 
B) ​conditional constraint 
C) ​mutually exclusive constraint 
D) ​corequisite constraint

Question 2

If the acceptance of project A is conditional on the acceptance of project B,and vice versa,the appropriate constraint to use is a

Accepted Answer

A) multiple-choice constraint. 
B) k out of n alternatives constraint. 
C) mutually exclusive constraint. 
D) corequisite constraint. 
A) multiple-choice constraint. 
B) k out of n alternatives constraint. 
C) mutually exclusive constraint. 
D) corequisite constraint.

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

Which of the following is the most useful contribution of integer programming?

Accepted Answer

A) finding whole number solutions where fractional solutions would not be appropriate 
B) using 0-1 variables for modeling flexibility 
C) increased ease of solution 
D) provision for solution procedures for transportation and assignment problems 
A) finding whole number solutions where fractional solutions would not be appropriate 
B) using 0-1 variables for modeling flexibility 
C) increased ease of solution 
D) provision for solution procedures for transportation and assignment problems

Question 5

​Integer linear programs are harder to solve than linear programs.

Accepted Answer

A) True 
 B)False

Question 6

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 7

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 8

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 9

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 10

The graph of a problem that requires x1 and x2 to be integer has a feasible region

Accepted Answer

A) the same as its LP relaxation. 
B) of dots. 
C) of horizontal stripes. 
D) of vertical stripes. 
A) the same as its LP relaxation. 
B) of dots. 
C) of horizontal stripes. 
D) of vertical stripes.

Question 11

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.

Question 12

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 13

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

Accepted Answer

A) True 
 B)False

Question 14

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 15

Consider a capital budgeting example with five projects from which to select.Let xi = 1 if project i is selected,0 if not,for i = 1,... ,5.Write the appropriate constraint(s)for each condition.Conditions are independent.
a.Choose no fewer than three projects.
b.If project 3 is chosen,project 4 must be chosen.
c.If project 1 is chosen,project 5 must not be chosen.
d.Projects cost 100,200,150,75,and 300 respectively.The budget is 450.
e.No more than two of projects 1,2,and 3 can be chosen.

Accepted Answer

Question 16

The Westfall Company has a contract to produce 10,000 garden hoses for a large discount chain.Westfall has four different machines that can produce this kind of hose.Because these machines are from different manufacturers and use differing technologies,their specifications are not the same.
​
 $$\begin{array} { c c c c } 
\text { Machine } & \begin{array} { c } 
\text { Fixed Cost to Set } \
\text { Up Production Run }
\end{array} & \begin{array} { c } 
\text { Variable Cost } \
\text { Per Hose }
\end{array} & \text { Capacity } \
\hline 1 & 750 & 1.25 & 6000 \
2 & 500 & 1.50 & 7500 \
3 & 1000 & 1.00 & 4000 \
4 & 300 & 2.00 & 5000
\end{array}$$ 
a.This problem requires two different kinds of decision variables.Clearly define each kind.
b.The company wants to minimize total cost.Give the objective function.
c.Give the constraints for the problem.
d.Write a constraint to ensure that if machine 4 is used,machine 1 cannot be.

Accepted Answer

a. Let @#LAT-DLM& the number of hoses pr

Question 17

Solve the following problem graphically.
​
a.Graph the constraints for this problem.Indicate all feasible solutions.
b.Find the optimal solution to the LP Relaxation.Round down to find a feasible integer solution.Is this solution optimal?
c.Find the optimal solution.

Accepted Answer

a.
The feasible region is those integer

Question 18

Solve the following problem graphically.
​
 $$\begin{array} { l l } 
\text { Min } & 6 X + 11 Y \
\text { s.t. } & 9 X + 3 Y \geq 27 \
& 7 X + 6 Y \geq 42 \
& 4 X + 8 Y \geq 32 \
& X , Y \geq 0 \text { and integer }
\end{array}$$ 
a.Graph the constraints for this problem.Indicate all feasible solutions.
b.Find the optimal solution to the LP Relaxation.Round up to find a feasible integer solution.Is this solution optimal?
c.Find the optimal solution.

Accepted Answer

a. The feasible region is the set of int

Question 19

Multiple choice constraints involve binary variables.

Accepted Answer

A) True 
 B)False

Question 20

In a model,x1 ≥ 0 and integer,x2 ≥ 0,and x3 = 0,1.Which solution would not be feasible?

Accepted Answer

A) x1 = 5,x2 = 3,x3 = 0 
B) x1 = 4,x2 = .389,x3 = 1 
C) x1 = 2,x2 = 3,x3 = .578 
D) x1 = 0,x2 = 8,x3 = 0 
A) x1 = 5,x2 = 3,x3 = 0 
B) x1 = 4,x2 = .389,x3 = 1 
C) x1 = 2,x2 = 3,x3 = .578 
D) x1 = 0,x2 = 8,x3 = 0

A requirement that two 0-1 variables both be either in or out of a solution together is a

If the acceptance of project A is conditional on the acceptance of project B,and vice versa,the appropriate constraint to use is a

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

Which of the following is the most useful contribution of integer programming?

Integer linear programs are harder to solve than linear programs.

Modeling a fixed cost problem as an integer linear program requires

Most practical applications of integer linear programming involve

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

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

The graph of a problem that requires x₁ and x₂ to be integer has a feasible region

Sensitivity analysis for integer linear programming

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.

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

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

Solve the following problem graphically. a.Graph the constraints for this problem.Indicate all feasible solutions. b.Find the optimal solution to the LP Relaxation.Round down to find a feasible integer solution.Is this solution optimal? c.Find the optimal solution.

Multiple choice constraints involve binary variables.

In a model,x₁ ≥ 0 and integer,x₂ ≥ 0,and x₃ = 0,1.Which solution would not be feasible?

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

A requirement that two 0-1 variables both be either in or out of a solution together is a​

If the acceptance of project A is conditional on the acceptance of project B,and vice versa,the appropriate constraint to use is a

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

Which of the following is the most useful contribution of integer programming?

​Integer linear programs are harder to solve than linear programs.

Modeling a fixed cost problem as an integer linear program requires

Most practical applications of integer linear programming involve

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

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

The graph of a problem that requires x1 and x2 to be integer has a feasible region

Sensitivity analysis for integer linear programming

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.

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

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

Solve the following problem graphically. ​ a.Graph the constraints for this problem.Indicate all feasible solutions. b.Find the optimal solution to the LP Relaxation.Round down to find a feasible integer solution.Is this solution optimal? c.Find the optimal solution.

Multiple choice constraints involve binary variables.

In a model,x1 ≥ 0 and integer,x2 ≥ 0,and x3 = 0,1.Which solution would not be feasible?

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

A requirement that two 0-1 variables both be either in or out of a solution together is a

Integer linear programs are harder to solve than linear programs.

The graph of a problem that requires x₁ and x₂ to be integer has a feasible region

Solve the following problem graphically. a.Graph the constraints for this problem.Indicate all feasible solutions. b.Find the optimal solution to the LP Relaxation.Round down to find a feasible integer solution.Is this solution optimal? c.Find the optimal solution.

In a model,x₁ ≥ 0 and integer,x₂ ≥ 0,and x₃ = 0,1.Which solution would not be feasible?