Question 1

The additivity assumption can be violated by nonlinear programming because of cross-product terms involving the product of two variables.

Accepted Answer

A) True 
 B)False

Question 2

In separable programming, if an activity violates the proportionality assumption it must have increasing marginal returns.

Accepted Answer

A) True 
 B)False

Question 3

The risk for a portfolio is decreased when the particular stocks tend to move up and down together.

Accepted Answer

A) True 
 B)False

Question 4

The members of the population used to create the next generation are picked randomly by the Evolutionary Solver.

Accepted Answer

A) True 
 B)False

Question 5

Note: This problem requires Excel.
A firm offers two different prices on its products, depending upon the quantity purchased. Since available resources are limited, the firm would like to prepare an optimal production plan to maximize profits. Product 1 has the following profitability: $75 each for the first 25 units and $60 for each unit over 25. Product 2's profitability is $200 each for the first 50 units and $100 each for each unit over 50. The products each require two raw materials to produce (see table below for usages and available quantities).
$$\begin{array} { | c | r | r | r | } 
\hline
\begin{array} { c } 
\text { Raw } \
\text { Material }
\end{array} & \begin{array} { c } 
\text { Praduct l usage } \
\text { (gallons per unit) }
\end{array} & \begin{array} { c } 
\text { Praduct 2 usage } \
\text { (gallons per unit) }
\end{array} & { \begin{array} { c } 
\text { Available Quantity } \
\text { (gallons) }
\end{array} } \
\hline \text { A } & 10 & 20 & 1,500 \
\hline \text { B } & 5 & 7 & 2,000 \
\hline
\end{array}$$
Use separable programming to find the optimal production plan.

Accepted Answer

A)  100 units Product 1, 100 units Product 2 
B)  50 units Product 1, 50 units Product 2 
C)  100 units Product 1, 25 units Product 2 
D)  25 units Product 1, 100 units Product 2 
E)  100 units Product 1, 50 units Product 2 
A)  100 units Product 1, 100 units Product 2 
B)  50 units Product 1, 50 units Product 2 
C)  100 units Product 1, 25 units Product 2 
D)  25 units Product 1, 100 units Product 2 
E)  100 units Product 1, 50 units Product 2

Question 6

Evolutionary Solver is often faster than the standard Solver at solving linear programming problems.

Accepted Answer

A) True 
 B)False

Question 7

If the RSPE Model Analysis indicates that the model is NLP Convex, then only the Evolutionary Solver can be counted on to yield near optimal solutions.

Accepted Answer

A) True 
 B)False

Question 8

If the slope of a graph never increases but sometimes decreases as the level of the activity increases, then it is said to have decreasing marginal returns.

Accepted Answer

A) True 
 B)False

Question 9

Which of the following profit functions has a logarithmic form?
I. x2 + 3x − 4
II. 4 ln x + 7
III. 3x − 4

Accepted Answer

A)  I only 
B)  II only 
C)  III only 
D)  I and II only 
E)  I, II, and III 
A)  I only 
B)  II only 
C)  III only 
D)  I and II only 
E)  I, II, and III

Question 10

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

A)  The chart shows a linear relationship. 
B)  The chart shows increasing marginal returns. 
C)  The chart shows a proportional relationship. 
D)  The chart shows discontinuities. 
E)  The chart is piecewise linear. 
A)  The chart shows a linear relationship. 
B)  The chart shows increasing marginal returns. 
C)  The chart shows a proportional relationship. 
D)  The chart shows discontinuities. 
E)  The chart is piecewise linear.

Question 11

After some experimentation, you have observed the following data concerning the relationship between marketing and sales. Use Excel's curve fitting method to find the best quadratic equation to model this relationship.
$\begin{array}{|l|c|c|c|c|c}
\hline \begin{array}{l}
\text { Marketing } \
(\$)
\end{array} & 100 & 110 & 120 & 130 & 140 \
\hline \begin{array}{l}
\text { Sales } \
(\$ 100)
\end{array} & 310 & 400 & 500 & 600 & 700 \
\hline
\end{array}
\begin{array}{|r|r|r|r|r|r|}
\hline \150 & 160 & 170 & 180 & 190 & 200 \
\hline \850 & 975 & 1,100 & 1,300 & 1,425 & 1,600 \
\hline
\end{array}$

Accepted Answer

A)  0.11x2 + 1.4x + 40 
B)  0.05x2 ? 1.1x ? 44 
C)  0.05x2 + 1.1x + 44 
D)  0.11x2 ? 1.4x ? 40 
E)  0.05x2 ? 1.1x + 44 
A)  0.11x2 + 1.4x + 40 
B)  0.05x2 ? 1.1x ? 44 
C)  0.05x2 + 1.1x + 44 
D)  0.11x2 ? 1.4x ? 40 
E)  0.05x2 ? 1.1x + 44

Question 12

Evolutionary Solver is best suited to which kinds of problems?

Accepted Answer

A)  Linear programs 
B)  Nonlinear programs with difficult objective functions 
C)  Nonlinear programs with decreasing marginal returns and no discontinuities 
D)  Nonlinear programs with many constraints 
E)  None of the choices is correct. 
A)  Linear programs 
B)  Nonlinear programs with difficult objective functions 
C)  Nonlinear programs with decreasing marginal returns and no discontinuities 
D)  Nonlinear programs with many constraints 
E)  None of the choices is correct.

Question 13

Excel's curve fitting method is used to find the values of the parameters for an equation that best fit data.

Accepted Answer

A) True 
 B)False

Question 14

If the RSPE Model Analysis indicates that the model is a NSP, then the GRG Nonlinear search method is the best one to use.

Accepted Answer

A) True 
 B)False

Question 15

Which of the following statements about Solver's Multistart option are TRUE?

Accepted Answer

A)  A nonlinear problem will always have the solution for any starting point. 
B)  Multistart always uses 100 random starting points. 
C)  Using Multistart guarantees that Solver will find the optimal solution. 
D)  Multistart may not find the optimal solution. 
E)  Multistart works well with functions such as "IF" and "ROUND." 
A)  A nonlinear problem will always have the solution for any starting point. 
B)  Multistart always uses 100 random starting points. 
C)  Using Multistart guarantees that Solver will find the optimal solution. 
D)  Multistart may not find the optimal solution. 
E)  Multistart works well with functions such as "IF" and "ROUND."

Question 16

In problems where the objective is to minimize the total cost of the activities, an activity is said to have decreasing marginal returns if the slope of its cost graph never increases but sometimes decreases as the level of the activity increases.

Accepted Answer

A) True 
 B)False

Question 17

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)  I only 
B)  II only 
C)  III only 
D)  I, II, and III 
E)  II and III only 
A)  I only 
B)  II only 
C)  III only 
D)  I, II, and III 
E)  II and III only

Question 18

When the marginal return from an activity decreases on a continuous basis, the profit graphs will consist of a series of line segments.

Accepted Answer

A) True 
 B)False

Question 19

Trying different starting points and picking the best solution will always yield the optimal solution to a nonlinear programming problem.

Accepted Answer

A) True 
 B)False

Question 20

If C1 is a changing cell, then ROUND(C1) is a linear function.

Accepted Answer

A) True 
 B)False

The additivity assumption can be violated by nonlinear programming because of cross-product terms involving the product of two variables.

In separable programming, if an activity violates the proportionality assumption it must have increasing marginal returns.

The risk for a portfolio is decreased when the particular stocks tend to move up and down together.

The members of the population used to create the next generation are picked randomly by the Evolutionary Solver.

Evolutionary Solver is often faster than the standard Solver at solving linear programming problems.

If the RSPE Model Analysis indicates that the model is NLP Convex, then only the Evolutionary Solver can be counted on to yield near optimal solutions.

If the slope of a graph never increases but sometimes decreases as the level of the activity increases, then it is said to have decreasing marginal returns.

Which of the following profit functions has a logarithmic form? I. x2 + 3x − 4 II. 4 ln x + 7 III. 3x − 4

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

Evolutionary Solver is best suited to which kinds of problems?

Excel's curve fitting method is used to find the values of the parameters for an equation that best fit data.

If the RSPE Model Analysis indicates that the model is a NSP, then the GRG Nonlinear search method is the best one to use.

Which of the following statements about Solver's Multistart option are TRUE?

In problems where the objective is to minimize the total cost of the activities, an activity is said to have decreasing marginal returns if the slope of its cost graph never increases but sometimes decreases as the level of the activity increases.

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.

When the marginal return from an activity decreases on a continuous basis, the profit graphs will consist of a series of line segments.

Trying different starting points and picking the best solution will always yield the optimal solution to a nonlinear programming problem.

If C1 is a changing cell, then ROUND(C1) is a linear function.

Introduction

Linear Programming: Basic Concepts

Linear Programming: Formulation and Applications

The Art of Modeling With Spreadsheets

What-If Analysis for Linear Programming

Network Optimization Problems

Using Binary Integer Programming to Deal With Yes-Or-No Decisions

Decision Analysis

Forecasting

Queueing Models

Computer Simulation: Basic Concepts

Computer Simulation With Analytic Solver

Filters

Exam 8: Nonlinear Programming

The additivity assumption can be violated by nonlinear programming because of cross-product terms involving the product of two variables.

In separable programming, if an activity violates the proportionality assumption it must have increasing marginal returns.

The risk for a portfolio is decreased when the particular stocks tend to move up and down together.

The members of the population used to create the next generation are picked randomly by the Evolutionary Solver.

Evolutionary Solver is often faster than the standard Solver at solving linear programming problems.

If the RSPE Model Analysis indicates that the model is NLP Convex, then only the Evolutionary Solver can be counted on to yield near optimal solutions.

If the slope of a graph never increases but sometimes decreases as the level of the activity increases, then it is said to have decreasing marginal returns.

Which of the following profit functions has a logarithmic form? I. x2 + 3x − 4 II. 4 ln x + 7 III. 3x − 4

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

Evolutionary Solver is best suited to which kinds of problems?

Excel's curve fitting method is used to find the values of the parameters for an equation that best fit data.

If the RSPE Model Analysis indicates that the model is a NSP, then the GRG Nonlinear search method is the best one to use.

Which of the following statements about Solver's Multistart option are TRUE?

In problems where the objective is to minimize the total cost of the activities, an activity is said to have decreasing marginal returns if the slope of its cost graph never increases but sometimes decreases as the level of the activity increases.

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.

When the marginal return from an activity decreases on a continuous basis, the profit graphs will consist of a series of line segments.

Trying different starting points and picking the best solution will always yield the optimal solution to a nonlinear programming problem.

If C1 is a changing cell, then ROUND(C1) is a linear function.

Introduction

Linear Programming: Basic Concepts

Linear Programming: Formulation and Applications

The Art of Modeling With Spreadsheets

What-If Analysis for Linear Programming

Network Optimization Problems

Using Binary Integer Programming to Deal With Yes-Or-No Decisions

Decision Analysis

Forecasting

Queueing Models

Computer Simulation: Basic Concepts

Computer Simulation With Analytic Solver

Filters