Question 1

Decreasing marginal returns violates which assumption of linear programming?

Accepted Answer

The proportionality assumption in linear programming implies that the output is directly proportional to the inputs. Decreasing marginal returns, where each additional unit of input produces less output than the previous unit, violates this assumption because it implies that the relationship between input and output is not constant.

Question 2

The following chart shows a relationship between advertising expenditures and sales.  Which of the following describes the chart in terms of a linear relationship?

Accepted Answer

The answer of The following chart shows a relationship between...

Question 3

Separable programming will always find the optimal solution when the following is true:

Accepted Answer

Separable programming requires both a piecewise linear profit or cost graph and decreasing marginal returns in order to find the optimal solution. If either of these conditions is not met, separable programming may not be able to find the optimal solution. Therefore, choice C is the best answer.

Question 4

If a model uses IF or ROUND functions that incorporate the changing cells, then running the RSPE Analyze Model without Solving feature will typically say the model is of what type?

Accepted Answer

The use of IF or ROUND functions indicates that the model is likely a Nonlinear Integer or Nonlinear Integer Mixed-Integer Programming (NSP or MINLP) problem, which is often difficult to solve using linear or convex optimization methods. The RSPE Analyze Model without Solving feature can identify the complexity of the model without actually attempting to find a solution.

Question 5

One reason that a manager may choose to use a nonlinear model to analyze a problem is

Accepted Answer

Nonlinear models are often used when there are complex relationships among variables or when the relationship between variables is not proportional. In such cases, using a linear model may not provide accurate results, and a nonlinear model may be a better choice for greater precision.

Question 6

The measure of risk for pairs of stocks in a portfolio selection problem is called:

Accepted Answer

The measure of risk for pairs of stocks in a portfolio selection problem is the covariance of the return. This measures how the returns of the two stocks move together. A high positive covariance means that the two stocks tend to move up and down together, while a high negative covariance means that they tend to move in opposite directions. The covariance, along with the expected return and individual variances, is used to calculate the efficient frontier of a portfolio.

Question 7

A nonlinear function may contain which of the following?
I. A term that contains a single variable with an exponent of 1.
II. A term that contains a single variable with an exponent of 2.
III. A term that is a constant times the product of two variables.

Accepted Answer

A nonlinear function can contain terms with exponents other than 1, including exponents of 2 or higher (II), and can also contain terms that involve products of variables, including constants multiplied by two variables (III). Therefore, all three options (I, II, and III) can be present in a nonlinear function, making choice D the correct answer.

Question 8

Which of the following techniques is appropriate when a nonlinear programming problem has multiple local optima?
I. Running Solver many times with different starting points.
II. Using the multistart feature to try different starting points.
III. Using Evolutionary Solver.

Accepted Answer

All three techniques are appropriate for dealing with nonlinear programming problems that have multiple local optima. Running Solver multiple times with different starting points, using the multistart feature, and employing Evolutionary Solver can all help in finding a global optimum by exploring the solution space from various initial conditions.

Question 9

The following chart shows a relationship between advertising expenditures and sales.  
Which of the following describes the chart in terms of a linear relationship?

Accepted Answer

The answer of The following chart shows a relationship between...

Question 10

The measure of risk in a portfolio selection problem is called:

Accepted Answer

The variance of the return measures the dispersion of possible returns around the expected value. A higher variance indicates a higher level of risk, as the portfolio's returns are more uncertain and could potentially be further from the expected value. Therefore, the measure of risk in a portfolio selection problem is the variance of the return.

Question 11

Which of the following can be part of a nonlinear profit graph?
I. Decreasing marginal returns.
II. Increasing marginal returns.
III. Discontinuities.

Accepted Answer

A nonlinear profit graph can include decreasing marginal returns, increasing marginal returns, and discontinuities. These elements can cause the graph to curve or have breaks, making it nonlinear.

Question 12

A nonlinear programming problem may have:
I. Activities with increasing marginal returns.
II. Activities with decreasing marginal returns.
III. Nonlinear functional constraints.

Accepted Answer

A nonlinear programming problem can have activities with increasing or decreasing marginal returns, and can also have nonlinear functional constraints. Therefore, all three statements are true and the correct answer is D.

Question 13

Evolutionary Solver is based on which of the following concepts?
I. Genetics.
II. Evolution.
III. Survival of the Fittest.

Accepted Answer

Evolutionary Solver is based on concepts from genetics (such as mutation and crossover), evolution (the process of change in a population), and the principle of survival of the fittest (whereby the best solutions are selected to continue). These principles guide the algorithm in exploring and optimizing solutions.

Question 14

The following chart shows a relationship between advertising expenditures and sales.  
Which of the following describes the chart in terms of a linear relationship?

Accepted Answer

The answer of The following chart shows a relationship between...

Question 15

Which of the following is an example of a nonlinear function?

Accepted Answer

The answer of Which of the following is an example...

Question 16

A linear function may contain which of the following?
I. A term that contains a single variable with an exponent of 1.
II. A term that contains a single variable with an exponent of 2.
III. A term that is a constant times the product of two variables.

Accepted Answer

A linear function has a degree of 1 which means it only contains variables with exponents of 1 or constants. This eliminates options II and III, leaving only option I as a valid characteristic of a linear function. Therefore, the correct answer is A) I only.

Question 17

Which of the following are disadvantages of the Evolutionary Solver?
I. It does not deal well with complicated objective functions.
II. It does perform well on models with many constraints.
III. It is easily trapped at local optima.

Accepted Answer

The answer of Which of the following are disadvantages of...

Question 18

Evolutionary Solver is best suited to which kinds of problems?

Accepted Answer

Evolutionary Solver is particularly effective for nonlinear programs with complex or difficult objective functions, as it uses mechanisms inspired by natural evolutionary processes to search for optimal solutions, making it well-suited to handle the complexities and peculiarities of such problems.

Question 19

The requirement that each term in the objective function only contains a single variable is in a linear program is referred to as:

Accepted Answer

The additivity assumption requires that each term in the objective function only contains a single variable. This means that there cannot be any products or powers of variables in the objective function, and each variable must appear only once in each term. This assumption allows the problem to be written in a standard form that can be solved using linear programming methods.

Question 20

Which of the following are advantages of the Evolutionary Solver?

Accepted Answer

The Evolutionary Solver is able to handle complex objective functions, making it a useful tool for optimization problems where traditional methods may struggle. However, it does not guarantee finding the optimal solution, nor is it necessarily faster than the standard Solver. Additionally, as with any solver, the solution it finds can vary depending on input parameters or initial conditions.

Quiz 8: Nonlinear Programming

Decreasing marginal returns violates which assumption of linear programming?

The following chart shows a relationship between advertising expenditures and sales. Which of the following describes the chart in terms of a linear relationship?

Separable programming will always find the optimal solution when the following is true:

If a model uses IF or ROUND functions that incorporate the changing cells, then running the RSPE Analyze Model without Solving feature will typically say the model is of what type?

One reason that a manager may choose to use a nonlinear model to analyze a problem is

The measure of risk for pairs of stocks in a portfolio selection problem is called:

A nonlinear function may contain which of the following? I. A term that contains a single variable with an exponent of 1. II. A term that contains a single variable with an exponent of 2. III. A term that is a constant times the product of two variables.

Which of the following techniques is appropriate when a nonlinear programming problem has multiple local optima? I. Running Solver many times with different starting points. II. Using the multistart feature to try different starting points. III. Using Evolutionary Solver.

The following chart shows a relationship between advertising expenditures and sales. Which of the following describes the chart in terms of a linear relationship?

The measure of risk in a portfolio selection problem is called:

Which of the following can be part of a nonlinear profit graph? I. Decreasing marginal returns. II. Increasing marginal returns. III. Discontinuities.

A nonlinear programming problem may have: I. Activities with increasing marginal returns. II. Activities with decreasing marginal returns. III. Nonlinear functional constraints.

Evolutionary Solver is based on which of the following concepts? I. Genetics. II. Evolution. III. Survival of the Fittest.

The following chart shows a relationship between advertising expenditures and sales. Which of the following describes the chart in terms of a linear relationship?

Which of the following is an example of a nonlinear function?

A linear function may contain which of the following? I. A term that contains a single variable with an exponent of 1. II. A term that contains a single variable with an exponent of 2. III. A term that is a constant times the product of two variables.

Which of the following are disadvantages of the Evolutionary Solver? I. It does not deal well with complicated objective functions. II. It does perform well on models with many constraints. III. It is easily trapped at local optima.

Evolutionary Solver is best suited to which kinds of problems?

The requirement that each term in the objective function only contains a single variable is in a linear program is referred to as:

Which of the following are advantages of the Evolutionary Solver?