Deck 7: Intro to Linear Programming

Question 1

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

Answer 1

False

Question 2

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

Answer 2

False

Question 3

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

Answer 3

True

Question 4

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

Question 5

A linear programming problem can be both unbounded and infeasible.

Question 6

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

Question 7

A redundant constraint is a binding constraint.

Question 8

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

Question 9

It is possible to have exactly two optimal solutions to a linear programming problem.

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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 15

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

Question 16

An unbounded feasible region might not result in an unbounded solution for a minimization or maximization problem.

Question 17

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

Question 18

An infeasible problem is one in which the objective function can be increased to infinity.

Question 19

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

Question 20

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

Question 21

​In what part(s)of a linear programming formulation would the decision variables be stated?

A)​objective function and the left-hand side of each constraint
B)​objective function and the right-hand side of each constraint
C)​the left-hand side of each constraint only
D)​the objective function only

Question 22

When you encounter infeasibility,making changes in the coefficients of the objective function will not help.

Question 23

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 24

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 25

​A redundant constraint results in

A)​no change in the optimal solution(s)
B)​an unbounded solution
C)​no feasible solution
D)​alternative optimal solutions

Question 26

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 27

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 28

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 29

The corner points of the feasible region represent alternative optimal solutions.
​

Question 30

Which of the following is a valid objective function for a linear programming problem?

A)Max 5xy
B)Min 4x + 3y + (2/3)z
C)Max 5x² + 6y²
D)Min (x₁ + x₂)/x₃

Question 31

​If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x₁)or 125 wiffle balls (x₂)can be produced per hour of labor,which of the following constraints reflects this situation?

A)​300x₁ + 125x₂ > 4,000
B)​300x₁ + 125x₂ < 4,000
C)​425(x₁ + x₂)< 4,000
D)​300x₁ + 125x₂ = 4,000

Question 32

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 33

A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called

A)optimal.
B)feasible.
C)infeasible.
D)semi-feasible.

Question 34

​The three assumptions necessary for a linear programming model to be appropriate include all of the following except

A)​proportionality
B)​additivity
C)​divisibility
D)​normality

Question 35

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 36

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 37

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 38

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 39

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 40

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 41

​Explain the steps necessary to put a linear program in standard form.

Question 42

​Explain the steps of the graphical solution procedure for a minimization problem.

Question 43

​A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality is

A)​a standard variable
B)​a slack variable
C)​a surplus variable
D)​a non-negative variable

Question 44

​Explain how to graph the line x₁ − 2x₂ ≥ 0.

Question 45

​Explain what to look for in problems that are infeasible or unbounded.

Question 46

​Explain the concepts of proportionality,additivity,and divisibility.

Question 47

​Explain the difference between profit and contribution in an objective function.Why is it important for the decision
maker to know which of these the objective function coefficients represent?

Question 48

​Create a linear programming problem with two decision variables and three constraints that will include both a slack
and a surplus variable in standard form.Write your problem in standard form.

Question 49

​Use a graph to illustrate why a change in an objective function coefficient does not necessarily lead to a change in
the optimal values of the decision variables,but a change in the right-hand sides of a binding constraint does lead to
new values.