Deck 2: Introduction to Linear Programming

Question 1

Linear programming is considered to be one of the most commonly used techniques for prescriptive analytics in business organizations.

Answer 1

True

Question 2

Linear programming is a mathematical programming approach in which at least the objective function or the constraints are assumed to be linear.

Answer 2

False

Question 3

The proportionality feature of linear programming models assumes that the contribution of decision variables to the objective function is proportional to their values.

Answer 3

True

Question 4

The proportionality feature of linear programming models assumes that the contribution of decision variables to each resource constraint is proportional to their values.

Question 5

The additivity feature of linear programming models assumes that the objective function can be calculated by adding the individual contributions of each decision variable.

Question 6

The additivity feature of linear programming models assumes that the usage of each constraint can be calculated by adding the individual usage of the constraint by each decision variable.

Question 7

In the case of maximization problems, the line representing the objective function is moved upward and parallel to itself until reaching the first point of contact with the area of feasible solution.

Question 8

In the case of minimization problems, the line representing the objective function is moved upward and parallel to itself until reaching the first point of contact with the area of feasible solution.

Question 9

Binding constraints are represented by lines that intersect at the point of the optimal solution.

Question 10

Resources represented by binding constraints are fully used by the optimal solution.

Question 11

Linear programming models have multiple solutions when the slope of the iso-profit line of the objective function differs from the slopes of each line representing any binding constraint.

Question 12

If the iso-profit line has the same slope as the line of a binding constraint, then the model has an infinite number of solutions.

Question 13

Linear programming models with infeasible solutions often arise in practice because management expectations are too high.

Question 14

Solver is a Microsoft Excel add-in used to successfully solve linear programming models only.

Question 15

Following a step-by-step approach to formulate and solve linear programming models helps practitioners to avoid complexity.

Question 16

Which of the following make linear programming (LP) a popular tool for data scientists?

A) LP structure allows practitioners to achieve goals despite limited resources.
B) LP models are easy to formulate.
C) LP models are easy to solve.
D) All of the above

Question 17

Which of the following is a business situation in which linear programming (LP) models can be used appropriately?

A) A manager of a production line wants to minimize the total production and inventory cost while meeting the sales demands for products.
B) A financial analyst wants to maximize the return on an investment with a limited budget for stocks and bonds.
C) A marketing manager wants to maximize the customer lifetime value with a limited advertising budget.
D) A logistics manager wants to minimize the total transportation cost for products and raw materials while meeting customer demands for those products.
E) All of the above business situations can be modeled with LP models.

Question 18

Which of the following is not a concept related to linearity?

A) Proportionality
B) Additivity
C) Feasibility
D) All of the above concepts are related to linearity.

Question 19

The proportionality feature of linear programming (LP) models assumes all of the following except that:

A) The contribution of decision variables to the objective function is proportional.
B) The contribution of decision variables to each resource is proportional.
C) The contribution of each decision variable can be added to obtain the overall value of the objective function.
D) All of the above are features of proportionality in LP.

Question 20

Which of the following is assumed when considering the additivity feature of linear programming (LP) models?

A) The contribution of decision variables to the objective function is proportional.
B) The contribution of decision variables to each resource is proportional.
C) The contribution of each decision variable can be added to obtain the overall value of the objective function.
D) All of the above are features of proportionality in LP.

Question 21

The additivity feature of linear programming (LP) models assumes all of the following except that:

A) The contribution of decision variables to the objective function is proportional.
B) The contribution of each decision variable can be added to obtain the overall usage of a given constraint.
C) The contribution of each decision variable can be added to obtain the overall value of the objective function.
D) All of the above are features of proportionality in LP.

Question 22

Which of the following is assumed when considering the linearity feature of linear programming (LP) models?

A) The contribution of decision variables to the objective function is proportional.
B) The contribution of each decision variable can be added to obtain the overall usage of a given constraint.
C) The contribution of each decision variable can be added to obtain the overall value of the objective function.
D) All of the above are features of proportionality in LP.

Question 23

Why it is important for a modeler to follow a step-by-step methodology when formulating linear programming models?

A) The modeler can avoid the complexity of the models.
B) The modeler can implement a "model less, iterate more" approach to improve the efficiency of the optimization algorithms.
C) The modeler can use the formulated model multiple times with newly calculated input parameters.
D) The modeler can fine-tune the model accordingly.

Question 24

Which of the following is not a major step when formulating linear programming models?

A) Defining decision variables
B) Defining the value of decision variables
C) Formulating the objective function
D) Identifying the set of constraints
E) Identifying the set of non-negativity constraints

Question 25

Which of the following is the most important reason for defining decision variables as part of linear programming (LP) formulation?

A) The decision variables will set the stage for the rest of the formulation steps.
B) The value of the decision variables will determine how many units will be produced at any given time.
C) The value of the decision variables will determine how many constraints are needed in the LP model.
D) The decision variables also determine how many goals the decision maker must achieve.

Question 26

Which of the following is not a suggested step when formulating an objective function?

A) Identifying a set of non-negativity constraints
B) Defining whether the goal is to maximize or minimize the objective function
C) Identifying contribution coefficients
D) Creating the equation for the objective function

Question 27

A maximization objective function could be used by the modeler in any of the following situations except:

A) When trying to optimize profit.
B) When trying to reach production levels.
C) When trying to improve customer satisfaction.
D) When trying to optimize cost.

Question 28

A minimization objective function could be used by the modeler in any of the following situations except:

A) When trying to optimize profit.
B) When trying to minimize production waste.
C) When trying to improve processing times.
D) When trying to optimize cost.

Question 29

Which of the following is not a major step when establishing constraints in a linear programming model?

A) Identifying the right-hand-side values for each resource
B) Calculating the left-hand-side value
C) Placing ? , = , or ? between the left- and right-hand-side values for each constraint
D) Identifying non-negativity constraints

Question 30

Which of the following is a situation in which ? (i.e., the less-than-or equal-to sign) must be used?

A) When a constraint represents the usage of available labor hours
B) When a constraint indicates that the manager wants to produce at least the ordered amount for a certain product
C) When a constraint indicates that the manager should not exceed the machine hours available
D) All of the above

Question 31

Which of the following is a situation in which ? (i.e., the greater-than-or-equal-to sign) must be used?

A) When a constraint represents the usage of available labor hours
B) When a constraint indicates that the manager wants to produce at least the ordered amount for a certain product
C) When a constraint indicates that the manager should not exceed the machine hours available
D) All of the above

Question 32

Which of the following situations is associated with a binding constraint in the solution of the linear programming model?

A) A binding constraint always has no slack (slack = 0).
B) A binding constraint always has slack (slack ? 0).
C) A binding constraint sometimes has negative slack (slack ? 0).
D) None of the above

Question 33

Which of the following situations is associated with a non-binding constraint in the solution of the linear programming model?

A) A non-binding constraint always has no slack (slack = 0).
B) A non-binding constraint always has slack (slack ? 0).
C) A non-binding constraint sometimes has negative slack (slack ? 0).
D) None of the above

Question 34

If funding is available to purchase additional resources, then a decision maker must recommend that the company invest in resources represented by:

A) A binding constraint.
B) A non-binding constraint.
C) A non-negativity constraint.
D) None of the above

Question 35

Linear programming models can result in:

A) A single solution.
B) Multiple solutions.
C) An infeasible solution.
D) All of the above

Question 36

Which of the following describes a situation in which linear programming models may result in unbounded solutions?

A) The model has many restrictions, and the constraints do not have a common feasible region.
B) The model has few restrictions, and the feasible region is not bounded by the model constraints.
C) The model has unrealistic goals, and the objective function cannot be maximized.
D) All of the above

Question 37

Which of the following describes a situation in which linear programming models result in infeasible solutions?

A) The model has many restrictions, and the constraints do not have a common feasible region.
B) The model has unrealistic goals, and the objective function cannot be maximized.
C) The model has unrealistic goals, and the objective function cannot be minimized.
D) All of the above

Question 38

The graphical approach to solving linear programming models:

A) Provides a visual and intuitive understanding of these models.
B) Provides a visual and intuitive understanding of the solution process.
C) Provides a visual demonstration the feasibility area.
D) Provides a visual understanding of the objective function.
E) All of the above are advantages of using the graphical approach.

Question 39

Which of the following steps can be used to solve a linear programming (LP) model graphically?

A) Graph the area of feasible solutions
B) Graph the objective function
C) Identify the coordinates for the optimal point
D) Identify the value of the objective function at the optimal solution
E) All of the above