Deck 2: Introduction to Linear Programming

Question 1

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

Answer 1

False

Question 2

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

Answer 2

True

Question 3

Because surplus variables represent the amount by which the solution exceeds a minimum target, they are given positive coefficients in the objective function.

Answer 3

False

Question 4

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

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 5

The improvement in the value of the objective function per unit increase in a right-hand side is the

A)sensitivity value.
B)dual price.
C)constraint coefficient.
D)slack value.

Question 6

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

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 7

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

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 8

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

Question 9

A redundant constraint is a binding constraint.

Question 10

Decision variables

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 11

All linear programming problems have all of the following properties EXCEPT

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 12

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

Question 13

Only binding constraints form the shape (boundaries) of the feasible region.

Question 14

A constraint that does not affect the feasible region is a

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

Question 15

Slack

A)is the difference between the left and right sides of a constraint.
B)is the amount by which the left side of a < constraint is smaller than the right side.
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 16

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

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

Question 17

In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.

Question 18

Which of the following statements is NOT true?

A)A feasible solution satisfies all constraints.
B)An optimal solution satisfies all constraints.
C)An infeasible solution violates all constraints.
D)A feasible solution point does not have to lie on the boundary of the feasible region.

Question 19

The maximization or minimization of a quantity is the

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

Question 20

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

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

Question 21

The standard form of a linear programming problem will have the same solution as the original problem.

Question 22

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.

Question 23

A range of optimality is applicable only if the other coefficient remains at its original value.

Question 24

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

Question 25

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

Question 26

Decision variables limit the degree to which the objective in a linear programming problem is satisfied.

Question 27

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

Question 28

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