Question 1

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 2

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

Accepted Answer

A) True 
 B)False  False

Question 3

The LP Relaxation contains the objective function and constraints of the IP problem, but drops all integer restrictions.

Accepted Answer

A) True 
 B)False

Question 4

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 5

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.E) B) and C)
F) None of the above

Question 6

If a problem has only less-than-or-equal-to constraints with positive coefficients for the variables, rounding down will always provide a feasible integer solution.

Accepted Answer

A) True 
 B)False

Question 7

The constraint x1 - x2 = 0 implies that if project 1 is selected, project 2 cannot be.

Accepted Answer

A) True 
 B)False  False

Question 8

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 9

Rounded solutions to linear programs must be evaluated for

Accepted Answer

A)  feasibility and optimality.
B)  sensitivity and duality.
C)  relaxation and boundedness.
D)  each of the above is true.E) All of the above
F) A) and D)

Question 10

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 11

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 problemsE) A) and D)
F) B) and D)

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

The 0-1 variables in the fixed cost models correspond to

Accepted Answer

A)  a process for which a fixed cost occurs.
B)  the number of products produced.
C)  the number of units produced.
D)  the actual value of the fixed cost.E) A) and C)
F) B) and D) A

Question 14

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.E) A) and C)
F) A) and D)

Question 15

Let x1 and x2 be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done.Which answer below indicates that project 2 can be done only if project 1 is done?

Accepted Answer

A)  x1 + x2 = 1
B)  x1 + x2 = 2
C)  x1 - x2 
D)  x1 - x2 > 0E) None of the above
F) A) and D)

Question 16

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.E) A) and D)
F) C) and D)

Question 17

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.E) A) and B)
F) A) and C)

Question 18

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 = 0E) A) and C)
F) B) and C)

Question 19

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

Accepted Answer

A) True 
 B)False

Question 20

If the optimal solutionASW8 to the LP relaxation problem is integer, it is the optimal solution to the integer linear program.

Accepted Answer

A) True 
 B)False

Exam 7: Integer Linear Programming

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.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedFalse

The LP Relaxation contains the objective function and constraints of the IP problem, but drops all integer restrictions.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Most practical applications of integer linear programming involve

Correct AnswerverifiedShow Answer

If a problem has only less-than-or-equal-to constraints with positive coefficients for the variables, rounding down will always provide a feasible integer solution.

Correct AnswerverifiedShow Answer

The constraint x1 - x2 = 0 implies that if project 1 is selected, project 2 cannot be.

Correct AnswerverifiedFalse

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.

Correct AnswerverifiedShow Answer

Rounded solutions to linear programs must be evaluated for

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

The 0-1 variables in the fixed cost models correspond to

Correct AnswerverifiedA

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

Correct AnswerverifiedShow Answer

Let x1 and x2 be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done.Which answer below indicates that project 2 can be done only if project 1 is done?

Correct AnswerverifiedShow Answer

Sensitivity analysis for integer linear programming

Correct AnswerverifiedShow Answer

Modeling a fixed cost problem as an integer linear program requires

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

If the optimal solutionASW8 to the LP relaxation problem is integer, it is the optimal solution to the integer linear program.

Correct AnswerverifiedShow Answer

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False

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The constraint x₁ - x₂ = 0 implies that if project 1 is selected, project 2 cannot be.

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False

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

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A

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Let x₁ and x₂ be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done.Which answer below indicates that project 2 can be done only if project 1 is done?

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

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