Question 1

A constraint that does not affect the feasible region is a

Accepted Answer

A)  non-negativity constraint.
B)  redundant constraint.
C)  standard constraint.
D)  slack constraint.

Question 2

Slack

Accepted Answer

A)  is the difference between the left and right sides of a constraint.
B)  is the amount by which the left side of a 
C)  is the amount by which the left side of a > constraint is larger than the right side.
D)  exists for each variable in a linear programming problem.

Question 3

A redundant constraint is a binding constraint.

Accepted Answer

A) True 
 B)False

Question 4

Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in

Accepted Answer

A)  standard form.
B)  bounded form.
C)  feasible form.
D)  alternative form.

Question 5

The constraint 5x1 - 2x2 < 0 passes through the point (20, 50).

Accepted Answer

A) True 
 B)False

Question 6

Alternative optimal solutions occur when there is no feasible solution to the problem.

Accepted Answer

A) True 
 B)False

Question 7

All linear programming problems have all of the following properties EXCEPT

Accepted Answer

A)  a linear objective function that is to be maximized or minimized.
B)  a set of linear constraints.
C)  alternative optimal solutions.
D)  variables that are all restricted to nonnegative values.

Question 8

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

Accepted Answer

A)  alternate optimality
B)  infeasibility
C)  unboundedness
D)  each case requires a reformulation.

Question 9

Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution.

Accepted Answer

A) True 
 B)False

Question 10

The point (3, 2) is feasible for the constraint 2x1 + 6x2 $ \leqslant$ 30.

Accepted Answer

A) True 
 B)False  True

Question 11

As long as the slope of the objective function stays between the slopes of the binding constraints

Accepted Answer

A)  the value of the objective function won't change.
B)  there will be alternative optimal solutions.
C)  the values of the dual variables won't change.
D)  there will be no slack in the solution.

Question 12

The maximization or minimization of a quantity is the

Accepted Answer

A)  goal of management science.
B)  decision for decision analysis.
C)  constraint of operations research.
D)  objective of linear programming. D

Question 13

All of the following statements about a redundant constraint are correct EXCEPT

Accepted Answer

A)  A redundant constraint does not affect the optimal solution.
B)  A redundant constraint does not affect the feasible region.
C)  Recognizing a redundant constraint is easy with the graphical solution method.
D)  At the optimal solution, a redundant constraint will have zero slack.

Question 14

To find the optimal solution to a linear programming problem using the graphical method

Accepted Answer

A)  find the feasible point that is the farthest away from the origin.
B)  find the feasible point that is at the highest location.
C)  find the feasible point that is closest to the origin.
D)  None of the alternatives is correct.

Question 15

Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side, a dual price cannot be negative.

Accepted Answer

A) True 
 B)False

Question 16

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

Accepted Answer

A) True 
 B)False

Question 17

No matter what value it has, each objective function line is parallel to every other objective function line in a problem.

Accepted Answer

A) True 
 B)False

Question 18

Decision variables

Accepted Answer

A)  tell how much or how many of something to produce, invest, purchase, hire, etc.
B)  represent the values of the constraints.
C)  measure the objective function.
D)  must exist for each constraint.

Question 19

In a feasible problem, an equal-to constraint cannot be nonbinding.

Accepted Answer

A) True 
 B)False  True

Question 20

The constraint 2x1 - x2 = 0 passes through the point (200,100).

Accepted Answer

A) True 
 B)False

Exam 2: Introduction to Linear Programming

A constraint that does not affect the feasible region is a

Correct AnswerverifiedShow Answer

Slack

Correct AnswerverifiedShow Answer

A redundant constraint is a binding constraint.

Correct AnswerverifiedShow Answer

Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in

Correct AnswerverifiedShow Answer

The constraint 5x1 - 2x2 < 0 passes through the point (20, 50).

Correct AnswerverifiedShow Answer

Alternative optimal solutions occur when there is no feasible solution to the problem.

Correct AnswerverifiedShow Answer

All linear programming problems have all of the following properties EXCEPT

Correct AnswerverifiedShow Answer

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

Correct AnswerverifiedShow Answer

Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution.

Correct AnswerverifiedShow Answer

The point (3, 2) is feasible for the constraint 2x1 + 6x2 ⩽ \leqslant⩽ 30.

Correct AnswerverifiedTrue

As long as the slope of the objective function stays between the slopes of the binding constraints

Correct AnswerverifiedShow Answer

The maximization or minimization of a quantity is the

Correct AnswerverifiedD

All of the following statements about a redundant constraint are correct EXCEPT

Correct AnswerverifiedShow Answer

To find the optimal solution to a linear programming problem using the graphical method

Correct AnswerverifiedShow Answer

Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side, a dual price cannot be negative.

Correct AnswerverifiedShow Answer

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

Correct AnswerverifiedShow Answer

No matter what value it has, each objective function line is parallel to every other objective function line in a problem.

Correct AnswerverifiedShow Answer

Decision variables

Correct AnswerverifiedShow Answer

In a feasible problem, an equal-to constraint cannot be nonbinding.

Correct AnswerverifiedTrue

The constraint 2x1 - x2 = 0 passes through the point (200,100).

Correct AnswerverifiedShow Answer

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The constraint 5x₁ - 2x₂ < 0 passes through the point (20, 50).

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The point (3, 2) is feasible for the constraint 2x₁ + 6x₂ $\leqslant$ 30.

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True

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D

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True

The constraint 2x₁ - x₂ = 0 passes through the point (200,100).

Correct Answer
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