Question 1

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

Accepted Answer

A) True 
 B)False

Question 2

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.

Question 3

If Project 5 must be completed before Project 6, the constraint would be x5- x6 $\le$ 0.

Accepted Answer

A) True 
 B)False

Question 4

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 5

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

Accepted Answer

A) True 
 B)False

Question 6

Simplon Manufacturing must decide on the processes to use to produce 1650 units. If machine 1 is used, its production will be between 300 and 1500 units. Machine 2 and/or machine 3 can be used only if machine 1's production is at least 1000 units. Machine 4 can be used with no restrictions.
  (HINT: Use an additional 0 - 1 variable to indicate when machines 2 and 3 can be used.)

Accepted Answer

The answer of Simplon Manufacturing must decide on the processes...

Question 7

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 $\le$ 0 
D)  x1-x2 $\ge$ 0

Question 8

Grush Consulting has five projects to consider. Each will require time in the next two quarters according to the table below.
  Revenue from each project is also shown. Develop a model whose solution would maximize revenue, meet the time budget of 25 in the first quarter and 20 in the second quarter, and not do both projects C and D.

Accepted Answer

The answer of Grush Consulting has five projects to consider....

Question 9

In a model involving fixed costs, the 0 - 1 variable guarantees that the capacity is not available unless the cost has been incurred.

Accepted Answer

A) True 
 B)False

Question 10

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.

Question 11

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.

Question 12

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.

Question 13

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

Question 14

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 15

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 16

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 these choices are true.

Question 17

In a model, x1 $\ge$ 0 and integer, x2 $\ge$ 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

Question 18

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

Accepted Answer

A) True 
 B)False

Question 19

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 20

If the LP relaxation of an integer program has a feasible solution, then the integer program has a feasible solution.

Accepted Answer

A) True 
 B)False

Exam 7: Integer Linear Programming

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

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

If Project 5 must be completed before Project 6, the constraint would be x₅- x₆ $\le$ 0.

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.

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

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?

In a model involving fixed costs, the 0 - 1 variable guarantees that the capacity is not available unless the cost has been incurred.

In an all-integer linear program,

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

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

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

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

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

Rounded solutions to linear programs must be evaluated for

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

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

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.

If the LP relaxation of an integer program has a feasible solution, then the integer program has a feasible solution.

Exam 7: Integer Linear Programming

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

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

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

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.

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

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?

In a model involving fixed costs, the 0 - 1 variable guarantees that the capacity is not available unless the cost has been incurred.

In an all-integer linear program,

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

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

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

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

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

Rounded solutions to linear programs must be evaluated for

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

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

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.

If the LP relaxation of an integer program has a feasible solution, then the integer program has a feasible solution.

If Project 5 must be completed before Project 6, the constraint would be x₅- x₆ $\le$ 0.

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

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?

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

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

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