Question 1

The graphical approach to solving linear programming models:

Accepted Answer

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. 
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 2

Linear programming models can result in:

Accepted Answer

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

Question 3

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.

Accepted Answer

A) True 
 B)False

Question 4

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

Accepted Answer

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. 
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 5

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

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

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. 
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 7

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

Accepted Answer

A) True 
 B)False

Question 8

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.

Accepted Answer

A) True 
 B)False

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

A) True 
 B)False

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

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

Accepted Answer

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 
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

Question 15

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

Accepted Answer

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. 
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 16

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

Accepted Answer

A) True 
 B)False

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

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

Accepted Answer

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 
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 19

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

Accepted Answer

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. 
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.

The graphical approach to solving linear programming models:

Linear programming models can result in:

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.

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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Exam 2: Introduction to Linear Programming

The graphical approach to solving linear programming models:

Linear programming models can result in:

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.

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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Business Analytics With Linear Programming

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