Question 1

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.

Accepted Answer

The answer of The additivity feature of linear programming (LP)...

Question 2

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.

Accepted Answer

The answer of Which of the following is assumed when...

Question 3

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.

Accepted Answer

The answer of Why it is important for a modeler...

Question 4

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

Accepted Answer

Defining the value of decision variables is not a major step in formulating linear programming models because the values of decision variables are determined as a result of solving the linear programming problem, not predefined in the formulation phase.

Question 5

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.

Accepted Answer

Decision variables are fundamental in linear programming as they represent the quantities to be determined by the solution of the LP problem. They are the foundation upon which the objective function and constraints are built, setting the stage for the entire formulation process.

Question 6

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

Accepted Answer

Identifying a set of non-negativity constraints is not a step in formulating an objective function itself but rather a step in formulating the constraints of a linear programming problem. The objective function formulation focuses on defining the goal (maximize or minimize), identifying contribution coefficients, and creating the equation.

Question 7

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.

Accepted Answer

Maximization is typically used for objectives like profit, production levels, or customer satisfaction, where the goal is to increase these metrics. Optimizing cost usually involves minimization, as the goal is to reduce costs, not increase them.

Question 8

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.

Accepted Answer

Minimization objective functions are used to reduce quantities, such as waste or time. Optimizing profit typically involves maximization, not minimization.

Question 9

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

Accepted Answer

The answer of Which of the following is not a...

Question 10

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

Accepted Answer

The answer of Which of the following is a situation...

Question 11

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

Accepted Answer

The greater-than-or-equal-to sign is used when a constraint requires meeting or exceeding a certain minimum value, such as producing at least the ordered amount.

Question 12

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

Accepted Answer

A binding constraint in linear programming is one where the final solution values for variables exactly satisfy the constraint's equation, leaving no slack. Slack represents the difference between the left-hand side and right-hand side of the constraint equation, and a slack of 0 means the constraint is exactly met without any surplus or deficit.

Question 13

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

Accepted Answer

A non-binding constraint in a linear programming model is one that does not hold the solution at its boundary, meaning the solution could vary without violating the constraint. This situation is characterized by the presence of slack (slack > 0), indicating that there is unused capacity or resources within the constraint.

Question 14

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

Accepted Answer

A binding constraint in optimization problems, including those related to resource allocation, directly limits the optimal solution. Investing in resources that are represented by a binding constraint can potentially improve the solution by relaxing the constraint, allowing for better utilization of resources and possibly enhancing overall performance or profit. Non-binding constraints do not limit the current solution, and non-negativity constraints are basic conditions that ensure variables do not take on negative values, which typically do not represent a direct opportunity for investment.

Question 15

Linear programming models can result in:
A) A single solution.
B) Multiple solutions.
C) An infeasible solution.
D) All of the above

Accepted Answer

Linear programming models can indeed result in a single solution, multiple solutions, or an infeasible solution, depending on the constraints and the objective function of the model.

Question 16

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

Accepted Answer

Linear programming models may result in unbounded solutions when the model has few restrictions and the feasible region is not bounded by the model constraints, allowing the objective function to increase indefinitely.

Question 17

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

Accepted Answer

Infeasibility in linear programming occurs when the constraints do not overlap to form a common feasible region, making it impossible to find a solution that satisfies all constraints.

Question 18

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.

Accepted Answer

The graphical approach to solving linear programming models offers a comprehensive visual and intuitive understanding of the models, the solution process, the feasibility area, and the objective function, making all the listed options correct advantages of using this method.

Question 19

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

Accepted Answer

All of the listed steps are part of the process to solve a linear programming model graphically. Graphing the feasible region, the objective function, identifying the optimal point, and determining the value of the objective function at this point are all essential steps in the graphical method of solving LP problems.

Quiz 2: Introduction to Linear Programming

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Linear programming models can result in:

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

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

The graphical approach to solving linear programming models:

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