Question 1

The objective function for an optimization problem is: Max 5x - 3y, with one of the constraints being x, y ≥ 0 and y integer. x and y are the only decisions variables. This is an example of a(n) _____.
A) all-integer linear program
B) mixed-integer linear program
C) LP relaxation of the integer linear program
D) binary integer linear program

Accepted Answer

If some, but not necessarily all, variables are required to be integer in a linear program, then it is a mixed-integer linear program.

Question 2

In cases where Excel Solver experiences excessive run times when solving integer linear problems, the Integer Optimality is set to _____.
A) 5%
B) 0%
C) infinity
D) a value equal to the number of integer constraints

Accepted Answer

If an optimal solution cannot be found within a reasonable amount of time, the Integer Optimality (%) can be reset to 5 percent or some higher value so that the search procedure may stop when a near optimal solution (within the tolerance of being optimal) has been found. In general, unless you are experiencing excessive run times, it is recommended that the Integer Optimality (%) is set to 0.

Question 3

The _____ of a set of points is the smallest intersection of linear inequalities that contain the set of points.
A) concave hull
B) slope
C) convex hull
D) geometry

Accepted Answer

The convex hull of a set of points is the smallest intersection of linear inequalities that contain the set of points.

Question 4

In binary integer linear program, the integer variables take only the values:
A) 0 or 1.
B) 0 or ∞.
C) 1 or ∞.
D) 1 or -1.

Accepted Answer

In binary integer linear program, the integer variables take only the values 0 or 1.

Question 5

_____ is a binary integer programming problem that involves choosing which possible projects or activities provide the best investment return.
A) Capital budgeting problem
B) Fixed-cost problem
C) Market share optimization problem
D) Location problem

Accepted Answer

Capital budgeting problem is a binary integer programming problem that involves choosing which possible projects or activities provide the best investment return.

Question 6

The linear program that results from dropping the integer requirements for the variables in an integer linear program is known as _____.
A) convex hull
B) a mixed-integer linear program
C) LP relaxation
D) a binary integer linear program

Accepted Answer

The linear program that results from dropping the integer requirements for the variables in an integer linear program is known as LP relaxation.

Question 7

In order to choose the best solution for implementation, practitioners usually recommend re-solving the integer linear program several times with variations in the_____.
A) objective function
B) decision variables
C) constraint coefficients
D) integer constraints

Accepted Answer

Because of the extreme sensitivity of the value of the optimal solution to the constraint coefficients, practitioners usually recommend re-solving the integer linear program several times with variations in the constraint coefficients before attempting to choose the best solution for implementation.

Question 8

The optimal solution to the integer program will be an extreme point of the _____.
A) convex hull
B) objective contour
C) cutting plane
D) slope

Accepted Answer

The optimal solution to the integer program will be an extreme point of the convex hull.

Question 9

Binary variables are identified with the _____designation in the Solver Parameters dialog box.
A) bin
B) 0 and 1
C) int
D) dif

Accepted Answer

Binary variables are identified with the bin designation in the Solver Parameters dialog box.

Question 10

Which of the following is true of the relationship between the value of the optimal integer solution and the value of the optimal solution to the LP Relaxation?
A) For integer linear programs involving minimization, the value of the optimal solution to the LP Relaxation provides an upper bound on the value of the optimal integer solution.
B) For integer linear programs involving maximization, the value of the optimal solution to the LP Relaxation provides a lower bound on the value of the optimal integer solution.
C) For integer linear programs involving minimization, the value of the optimal solution to the LP Relaxation provides a lower bound on the value of the optimal integer solution.
D) For any linear program involving either minimization or maximization, the value of the optimal solution to the LP Relaxation provides an infeasible value for the optimal integer solution.

Accepted Answer

For integer linear programs involving minimization, the value of the optimal solution to the LP Relaxation provides a lower bound on the value of the optimal integer solution.

Question 11

Which of the following approaches to solving integer linear optimization problems tries to identify the convex hull by adding a series of new constraints that do not exclude any feasible integer points?
A) Branch-and bound approach
B) Cutting plane approach
C) Trial-and-error approach
D) Convex hull approach

Accepted Answer

Cutting plane approaches try to identify the convex hull by adding a series of new constraints that do not exclude any feasible integer points.

Question 12

Which of the following is true about the sensitivity analysis for integer optimization problems?
A) Sensitivity reports are readily available for integer optimization problems similar to the linear programming problems.
B) Because of the discrete nature of the integer optimization, Excel Solver takes much more time to calculate objective function coefficient ranges, shadow prices, and right-hand-side ranges.
C) The sensitivity analysis is not important for integer problems.
D) To determine the sensitivity of the solution to changes in model inputs for integer optimization problems, the data must be changed and the problem must be re-solveD)

Accepted Answer

Sensitivity reports are not available for integer optimization problems. To determine the sensitivity of the solution to changes in model inputs, you must change the data and re-solve the problem.

Question 13

The objective function for a linear optimization problem is: Max 3x + 5y, with one of the constraints being x, y ≥ 0 and integer. x and y are the only decisions variables. This is an example of a(n) _____.
A) all-integer linear program
B) mixed-integer linear program
C) nonlinear program
D) binary integer linear program

Accepted Answer

If all variables are required to be integer in a linear program, then it is an all-integer linear program.

Question 14

The imposition of integer restriction is necessary for models where:
A) nonnegativity constraints are needed.
B) variables can take negative values.
C) the decision variables cannot take fractional values.
D) possible values of variables are restricted to particular intervals.

Accepted Answer

The imposition of integer restriction is necessary for models where the decision variables cannot take fractional values.

Question 15

The _____ approach to solving integer linear optimization problems breaks the feasible region of the LP Relaxation into subregions until the subregions have integer solutions or it is determined that the solution cannot be in the subregion.
A) cutting plane
B) trial-and-error
C) breaking region
D) branch-and-bound

Accepted Answer

The branch-and-bound approach to solving integer linear optimization problems breaks the feasible region of the LP Relaxation into subregions until the subregions have integer solutions or it is determined that the solution cannot be in the subregion.

Question 16

The importance of _____ for integer linear programming problems is often intensified by the fact that a small change in one of the coefficients in the constraints can cause a relatively large change in the value of the optimal solution.
A) objective function
B) decision variables
C) sensitivity analysis
D) optimization analysis

Accepted Answer

Sensitivity analysis often is more crucial for integer linear programming problems than for linear programming problems. A small change in one of the coefficients in the constraints can cause a relatively large change in the value of the optimal solution.

Question 17

The worksheet formulation for integer linear programs and linear programming problems is exactly the same except that the _____ for integer linear programs.
A) objective function using Set Objective in the Solver Parameters dialog box is set to Value Of option
B) decision variables need not be added in By Changing Variable Cells in the Solver Parameters dialog box
C) decision variables must be added in By Changing Variable Cells in the Solver Parameters dialog box along with selecting the Ignore Integer Constraints in the Integer Options dialog box
D) constraints must be added in the Solver Parameters dialog box to identify the integer variables and the value for Tolerance in the Integer Options dialog box may need to be adjusted

Accepted Answer

The worksheet formulation for integer linear programs is similar to that for linear programming problems. Actually the worksheet formulation is exactly the same, but some additional information must be provided when setting up the Solver Parameters and Options dialog boxes. Constraints must be added in the Solver Parameters dialog box to identify the integer variables. In addition, the value for Tolerance in the Integer Options dialog box may need to be adjusted to obtain a solution.

Question 18

Which of the following is true of rounding the solution to an integer?
A) It always produces the most optimal integer solution.
B) It never produces a feasible solution.
C) It does not affect the objective function.
D) It may or may not be feasible.

Accepted Answer

Rounding to an integer solution is a trial-and-error approach. Each rounded solution must be evaluated for feasibility as well as for its impact on the value of the objective function. Even when a rounded solution is feasible, we do not have a guarantee that we have found the optimal integer solution.

Question 19

The objective function for a linear optimization problem is: Max 3x + 2y, with one of the constraints being x, y = 0, 1. x and y are the only decision variables. This is an example of a _____.
A) nonlinear program
B) mixed-integer linear program
C) LP relaxation of the integer linear program
D) binary integer linear program

Accepted Answer

In some applications, the integer variables may take on only the values 0 or 1. Then we have a binary integer linear program.

Question 20

The objective function for an optimization problem is: Min 3x - 2y, with one of the constraints being x, y ≥ 0 and integer. If the integer restriction on the variables is removed, this would be a familiar two-variable linear program; however, it would be an example of _____.
A) convex hull of the linear program
B) a mixed-integer linear program
C) LP relaxation of the integer linear program
D) a binary integer linear program

Accepted Answer

The linear program that results from dropping the integer requirements for the variables in an integer linear program is known as LP relaxation.

Quiz 9: Integer Linear Optimization Models

The objective function for an optimization problem is: Max 5x - 3y, with one of the constraints being x, y ≥ 0 and y integer. x and y are the only decisions variables. This is an example of a(n) _____.

In cases where Excel Solver experiences excessive run times when solving integer linear problems, the Integer Optimality is set to _____.

The _____ of a set of points is the smallest intersection of linear inequalities that contain the set of points.

In binary integer linear program, the integer variables take only the values:

_____ is a binary integer programming problem that involves choosing which possible projects or activities provide the best investment return.

The linear program that results from dropping the integer requirements for the variables in an integer linear program is known as _____.

In order to choose the best solution for implementation, practitioners usually recommend re-solving the integer linear program several times with variations in the_____.

The optimal solution to the integer program will be an extreme point of the _____.

Binary variables are identified with the _____designation in the Solver Parameters dialog box.

Which of the following is true of the relationship between the value of the optimal integer solution and the value of the optimal solution to the LP Relaxation?

Which of the following approaches to solving integer linear optimization problems tries to identify the convex hull by adding a series of new constraints that do not exclude any feasible integer points?

Which of the following is true about the sensitivity analysis for integer optimization problems?

The objective function for a linear optimization problem is: Max 3x + 5y, with one of the constraints being x, y ≥ 0 and integer. x and y are the only decisions variables. This is an example of a(n) _____.

The imposition of integer restriction is necessary for models where:

The _____ approach to solving integer linear optimization problems breaks the feasible region of the LP Relaxation into subregions until the subregions have integer solutions or it is determined that the solution cannot be in the subregion.

The importance of _____ for integer linear programming problems is often intensified by the fact that a small change in one of the coefficients in the constraints can cause a relatively large change in the value of the optimal solution.

The worksheet formulation for integer linear programs and linear programming problems is exactly the same except that the _____ for integer linear programs.

Which of the following is true of rounding the solution to an integer?

The objective function for a linear optimization problem is: Max 3x + 2y, with one of the constraints being x, y = 0, 1. x and y are the only decision variables. This is an example of a _____.

The objective function for an optimization problem is: Min 3x - 2y, with one of the constraints being x, y ≥ 0 and integer. If the integer restriction on the variables is removed, this would be a familiar two-variable linear program; however, it would be an example of _____.