Deck 4: Business Analytics With Nonlinear Programming

Question 1

Nonlinear programming models are based on the assumptions that the objective function and constraints are nonlinear equations.

Answer 1

False

Question 2

Business situations often have relationships that are often not proportional or additive.

Answer 2

True

Question 3

Nonlinear programming models have the same structure as the linear programming models. Both models consist of the objective function, a set of constraints, and a set of non-negativity constraints.

Answer 3

True

Question 4

Relationships in nonlinear programming models with two decision variables can be represented by straight lines.

Question 5

A local optimum is a point in the feasible region with a better value than any other feasible point in the small neighborhood around it.

Question 6

A global optimum is a point in the feasible region with a better value than any other feasible point in the entire area of feasible solutions.

Question 7

When constraints are nonlinear, any local optimum is also a global optimum.

Question 8

When an objective function is nonlinear, any local optimum is also a global optimum.

Question 9

Formulation steps for nonlinear programming models are identical to those of linear programming models.

Question 10

The reduced gradient values in sensitivity analysis for nonlinear programming models are valid only at the point of the optimal solution.

Question 11

The Lagrange multiplier values in sensitivity analysis for nonlinear programming models are valid only at the point of the optimal solution.

Question 12

When solving linear or nonlinear programming models, a constraint with a zero slack variable is a binding constraint.

Question 13

A modeler may check the "Use Multistart" box under "Options" to allow Solver to avoid the local optimum as much as possible.

Question 14

The availability of more data allows organizations to explore, formulate, and solve previously unsolvable problems.

Question 15

In the era of Big Data, advanced software programs such as Solver can be used to navigate large number variables and constraints.

Question 16

A nonlinear model has at least one nonlinear equation in either the constraint or the objective function.

Question 17

Solver's GRG algorithm is best suited for linear programming models.

Question 18

When using nonlinear programming models, there is always a risk that the algorithm will result in a local optimum.

Question 19

Mathematical modeling of real-world business situations involves:

A) Linear relationships in the objective functions.
B) Linear relationships of resource constraints.
C) Nonlinear relationships in the objective functions.
D) Nonlinear relationships of resource constraints.
E) All of the above

Question 20

Which of the following must be satisfied in a nonlinear programming model?

A) The objective function must be nonlinear.
B) The constraints must be nonlinear equations.
C) Either a or b
D) Neither a nor b

Question 21

By definition, any linear equation must be:

A) Proportional and additive.
B) Proportional or additive.
C) Neither proportional nor additive.
D) Either non-proportional or non-additive.

Question 22

The proportionality assumption may fail under certain conditions such as:

A) Economies of scale.
B) Buy one, get a second item of an equal or lower price for free.
C) Both a and b
D) Neither a nor b

Question 23

The additivity assumption may fail under certain conditions such as:

A) Economies of scale
B) Buy one, get a second item of an equal or lower price for free.
C) Both a and b
D) Neither a nor b

Question 24

If the objective function or any of the constraints do not follow the proportionality or additivity requirement, then the decision maker may choose to represent business relationships with a:

A) Regression model.
B) Nonlinear programming model.
C) Linear programming model.
D) None of the above

Question 25

Which of the following is not a part of the nonlinear programming formulation?

A) An objective function to be optimized
B) A set of constraints to be satisfied
C) A set of nonlinear objectives to be sought
D) All of the above are components of nonlinear programming formulations.

Question 26

Nonlinear programming models are usually:

A) More challenging to solve than linear programming models.
B) Less representative of real-world problems.
C) Less accurate in the results of the final solution.
D) All of the above distinguish nonlinear programming from linear programming counterparts.

Question 27

In certain situations, a decision maker may decide to ignore the assumptions of nonlinearity when formulating a model in exchange for:

A) More accurate results of the solution.
B) A simpler formulation and solution process.
C) A better representation of real-world relationships.
D) All of the above

Question 28

In certain situations, a decision maker may choose nonlinear programming models in exchange for:

A) More accurate results of the solution.
B) A simpler formulation process.
C) A simpler solution process.
D) All of the above

Question 29

Relationships in linear programming models can be represented by:

A) Straight lines when the model has two decision variables.
B) Planes when the model has three decision variables.
C) Both a and b are true.
D) None of the above

Question 30

Nonlinear relationships in nonlinear programming models can be represented by:

A) Straight lines when the model has two decision variables.
B) Planes when the model has three decision variables.
C) Both a and b are true.
D) None of the above

Question 31

Nonlinear relationships in nonlinear programming models can be represented by:

A) Curved lines when the model has two decision variables.
B) Planes when the model has three decision variables.
C) Both a and b are true.
D) None of the above

Question 32

Solving nonlinear programming models may be more difficult than solving linear programming models because:

A) Nonlinear constraints may create discontinuous areas that satisfy all constraints.
B) Nonlinear constraints are difficult to translate into mathematical functions.
C) Nonlinear constraints are associated with a quantity discount.
D) All of the above

Question 33

Which of the following is a step for formulating nonlinear programming models?

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

Question 34

Which of the following is a step for solving nonlinear programming models?

A) Creating an Microsoft Excel template
B) Applying Solver
C) Interpreting the solution results
D) All of the above

Question 35

The final value in the variable cells of the sensitivity report of nonlinear programming models can indicate:

A) The initial solution for the decision variables.
B) The optimal solution for the decision variables.
C) A range of optimal solutions for the decision variables.
D) Any of the above

Question 36

Which of the following distinguishes the sensitivity reports of nonlinear programming models from the sensitivity reports of regular linear programming models?

A) The "reduced cost" in linear programming models is called the "Lagrange multiplier" in nonlinear programming models.
B) The "shadow price" in linear programming models is called the "reduced gradient" in nonlinear programming models.
C) The "reduced cost" in linear programming models is called the "reduced gradient" in nonlinear programming models.
D) All of the above

Question 37

The dual values in sensitivity analysis for nonlinear programming models:

A) Change when these values move away from the optimal solution.
B) Remain constant within the range between the upper and lower limits.
C) Become invalid at the point of the optimal solution.
D) None of the above statements are true about the dual values for nonlinear programming models.

Question 38

Which of the following dimensions of Big Data offers increased opportunities for optimization models in general and nonlinear programming models in particular?

A) Volume
B) Variety
C) Velocity
D) All of the above

Question 39

Which of the following is a good option for the decision maker when formulating and solving complex nonlinear programming models?

A) Formulating the problem as a linear model and considering the trade-off between a less rigorous formulation and an efficient solution
B) Formulating the problem as a nonlinear model and solving it using linear modeling approaches
C) Not using an optimization technique and saving on model building and solution costs
D) All of the above

Question 40

Solutions of nonlinear programming models with Microsoft Excel will often generate "division by zero" errors. To avoid these errors, the decision maker should:

A) Ignore them and read the solution as provided by Excel.
B) Accept the errors as part of the solution (i.e., there is no solution to the given problem).
C) Add a non-negativity constraint for decision variables instead of checking the non-negativity box in Solver.
D) All of the above