Question 1

The Nonlinear Solver keeps track of a large set of candidate solutions, called the population.

Accepted Answer

A) True 
 B)False  False

Question 2

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.
$\begin{array}{|l|l|l|l|l|l|}
\hline \begin{array}{l}
\text { Marketing } \
(\$)
\end{array} & 100 & 110 & 120 & 130 & 140 \
\hline \begin{array}{l}
\text { Sales } \
(\$ 100)
\end{array} & 310 & 500 & 600 & 690 & 780 \
\hline
\end{array}
\begin{array}{r|r|r|r|r|r|}
\hline \150 & 160 & 170 & 180 & 190 & 200 \
\hline \850 & 925 & 1,000 & 1,050 & 1,09 & 1,120 \
\hline
\end{array}$

Accepted Answer

A)  ?0.055x2 + 24x ? 1516 
B)  0.055x2 + 24x ? 1516 
C)  ?0.055x2 ? 24x ? 1516 
D)  ?0.055x2 + 24x + 1516 
E)  ?0.11x2 + 24x ? 1516 
A)  ?0.055x2 + 24x ? 1516 
B)  0.055x2 + 24x ? 1516 
C)  ?0.055x2 ? 24x ? 1516 
D)  ?0.055x2 + 24x + 1516 
E)  ?0.11x2 + 24x ? 1516 A

Question 3

Note: This problem requires Excel.
The marketing department has determined that the relationship between marketing expenditures (x) and sales can be modelled by the equation Sales = 100x − x2 + 20. Use a Nonlinear Solver tool to determine the level of marketing expenditure that will maximize sales.

Accepted Answer

A)  40 
B)  50 
C)  60 
D)  70 
E)  80 
A)  40 
B)  50 
C)  60 
D)  70 
E)  80 B

Question 4

If C1:C6 are all changing cells, then SUMPRODUCT(C1:C3, C4:C6) is a linear function.

Accepted Answer

A) True 
 B)False

Question 5

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

Accepted Answer

A)  the covariance of the return. 
B)  the variance of the return. 
C)  the expected return. 
D)  decreasing marginal return. 
E)  None of the choices is correct. 
A)  the covariance of the return. 
B)  the variance of the return. 
C)  the expected return. 
D)  decreasing marginal return. 
E)  None of the choices is correct.

Question 6

If the data cells are in column D and the changing cells are in column C, which of the following are linear formulas in a spreadsheet?
I. =SUMPRODUCT(D1:D6, C1:C6)
II. =SUMPRODUCT(C1:C3, C4:C6)
III. =SUM(C1:C6)

Accepted Answer

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

Question 7

Which of the following statements about solving maximization problems with Excel's Nonlinear Solver?
I. Nonlinear Solver will always find the global maximum.
II. Nonlinear Solver will always find a local maximum but not necessarily the global maximum.
III. With diminishing returns, Nonlinear Solver will always find the global maximum.

Accepted Answer

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

Question 8

If the RSPE Model Analysis indicates that the model is quadratic, which of the following is TRUE?

Accepted Answer

A)  The model can be solved using linear programming tools. 
B)  The Evolutionary Solver will always find the optimal solution. 
C)  Using the Nonlinear Solver will never find the optimal solution. 
D)  The model contains functions such as "IF" or "ROUND." 
E)  None of the choices is true. 
A)  The model can be solved using linear programming tools. 
B)  The Evolutionary Solver will always find the optimal solution. 
C)  Using the Nonlinear Solver will never find the optimal solution. 
D)  The model contains functions such as "IF" or "ROUND." 
E)  None of the choices is true.

Question 9

If D1 is a data cell, and C1 and C2 are changing cells, then IF(D1 >= 2, C1, C2) is a linear function.

Accepted Answer

A) True 
 B)False

Question 10

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)  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 11

Note: This problem requires Excel.
You have noticed that paying higher wages attracts more productive employees. However, you are concerned that there may be a limit to this relationship. Some experimentation has convinced you that the relationship between daily wages paid (x) and profits can be modelled by the equation Profit = 50x − 0.5x2 + .001x3 + 200. The range of wages you are willing to consider is from $0 to $500 per day. Use the Evolutionary Solver tool to determine the level of wages that will maximize profits.

Accepted Answer

A)  200 
B)  300 
C)  400 
D)  500 
E)  Cannot be determined 
A)  200 
B)  300 
C)  400 
D)  500 
E)  Cannot be determined

Question 12

Note: This problem requires Excel.
You have noticed that paying higher wages attracts more productive employees. However, you are concerned that there may be a limit to this relationship. Some experimentation has convinced you that the relationship between wages paid (x) and profits can be modelled by the equation Profit = 25x − 0.1x2 + 200. Use a Nonlinear Solver tool to determine the level of wages that will maximize profits.

Accepted Answer

A)  25 
B)  50 
C)  75 
D)  100 
E)  125 
A)  25 
B)  50 
C)  75 
D)  100 
E)  125

Question 13

The additivity assumption of linear programming states that each term in the objective function is the sum of two or more variables.

Accepted Answer

A) True 
 B)False

Question 14

If a problem can be modelled as a separable program with three line segments, how many decision variables is it likely to have?

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  Only 1 or 2 
E)  1, 2, or 3 
A)  1 
B)  2 
C)  3 
D)  Only 1 or 2 
E)  1, 2, or 3

Question 15

Which of the following profit functions has a quadratic form?
I. x2 + 3x − 4
II. 3x2 + 4x + 6
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 16

The following chart shows the relationship between marketing and sales.   Which of the following statements is TRUE?
I. There is a local minimum when marketing expenditure equals $120.
II. There is a local maximum when marketing expenditure equals $120.
III. There is a global maximum when marketing expenditure equals $160.

Accepted Answer

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

Question 17

Note: This problem requires Excel.
A firm offers three 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: $10 each for the first 50 units, $9 each for units 51-100, and $8 for each unit over 100. Product 2's profitability is $20 each for the first 25 units, $19 each for units 26-50, and $18 each for each unit over 50. The products each require 3 raw materials to produce (see table below for usages and available quantities).
$\begin{array}{|c|r|r|r|}
\hline
\begin{array}{c}
\text { Raw } \
\text { Material }
\end{array} & \begin{array}{c}
\text { Product 1 usage } \
\text { (pounds per unit) }
\end{array} & \begin{array}{c}
\text { Product 2 usage } \
\text { (pounds per unit) }
\end{array} & \begin{array}{c}
\text { Available Quantity } \
\text { (pounds) }
\end{array} \
\hline \text { A } & 5 & 12 & 1,000 \
\hline \text { B } & 4 & 10 & 2,000 \
\hline \text { C } & 7 & 6 & 1,500 \
\hline
\end{array}$
Use separable programming to find the optimal production plan.

Accepted Answer

A)  100 units Product 1, 100 units Product 2 
B)  100 units Product 1, 50 units Product 2 
C)  140 units Product 1, 25 units Product 2 
D)  25 units Product 1, 140 units Product 2 
E)  100 units Product 1, 140 units Product 2 
A)  100 units Product 1, 100 units Product 2 
B)  100 units Product 1, 50 units Product 2 
C)  140 units Product 1, 25 units Product 2 
D)  25 units Product 1, 140 units Product 2 
E)  100 units Product 1, 140 units Product 2

Question 18

The following chart shows the relationship between marketing and sales.   Which of the following statements is TRUE?
I. There is a local maximum when marketing expenditure equals $120.
II. There is a local minimum when marketing expenditure equals $140.
III. There is a local maximum when marketing expenditure equals $160.

Accepted Answer

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

Question 19

Which of the following are advantages of the Evolutionary Solver?

Accepted Answer

A)  The complexity of the objective function does not matter. 
B)  It will always find the optimal solution. 
C)  It is faster than the standard Solver. 
D)  It always finds the same solution. 
E)  None of the choices is correct. 
A)  The complexity of the objective function does not matter. 
B)  It will always find the optimal solution. 
C)  It is faster than the standard Solver. 
D)  It always finds the same solution. 
E)  None of the choices is correct.

Question 20

Profit = 3x1 + 2x2 + 9x1x2 is an example of a nonlinear function.

Accepted Answer

A) True 
 B)False

The Nonlinear Solver keeps track of a large set of candidate solutions, called the population.

If C1:C6 are all changing cells, then SUMPRODUCT(C1:C3, C4:C6) is a linear function.

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

If the data cells are in column D and the changing cells are in column C, which of the following are linear formulas in a spreadsheet? I. =SUMPRODUCT(D1:D6, C1:C6) II. =SUMPRODUCT(C1:C3, C4:C6) III. =SUM(C1:C6)

If the RSPE Model Analysis indicates that the model is quadratic, which of the following is TRUE?

If D1 is a data cell, and C1 and C2 are changing cells, then IF(D1 >= 2, C1, C2) is a linear function.

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

The additivity assumption of linear programming states that each term in the objective function is the sum of two or more variables.

If a problem can be modelled as a separable program with three line segments, how many decision variables is it likely to have?

Which of the following profit functions has a quadratic form? I. x2 + 3x − 4 II. 3x2 + 4x + 6 III. 3x − 4

Which of the following are advantages of the Evolutionary Solver?

Profit = 3x1 + 2x2 + 9x1x2 is an example of a nonlinear 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 Nonlinear Solver keeps track of a large set of candidate solutions, called the population.

If C1:C6 are all changing cells, then SUMPRODUCT(C1:C3, C4:C6) is a linear function.

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

If the data cells are in column D and the changing cells are in column C, which of the following are linear formulas in a spreadsheet? I. =SUMPRODUCT(D1:D6, C1:C6) II. =SUMPRODUCT(C1:C3, C4:C6) III. =SUM(C1:C6)

If the RSPE Model Analysis indicates that the model is quadratic, which of the following is TRUE?

If D1 is a data cell, and C1 and C2 are changing cells, then IF(D1 >= 2, C1, C2) is a linear function.

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

The additivity assumption of linear programming states that each term in the objective function is the sum of two or more variables.

If a problem can be modelled as a separable program with three line segments, how many decision variables is it likely to have?

Which of the following profit functions has a quadratic form? I. x2 + 3x − 4 II. 3x2 + 4x + 6 III. 3x − 4

Which of the following are advantages of the Evolutionary Solver?

Profit = 3x1 + 2x2 + 9x1x2 is an example of a nonlinear 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