Question 1

If the coefficient of each squared term in a quadratic function is positive, the function is

Accepted Answer

A) concave. 
B) convex. 
C) elliptical. 
D) sinusoidal. 
A) concave. 
B) convex. 
C) elliptical. 
D) sinusoidal. B

Question 2

Skooter's Skateboards produces two models of skateboards, the FX and the ZX. Skateboard revenue (in $l,000s) for the firm is nonlinear and is stated as (number of FXs)(5-0.2 number of FXs) + (number of ZXs)(7 - 0.3 number of ZXs). Skooter's has 80 labor-hours available per week in its paint shop. Each FX requires 2 labor-hours to paint and each ZX requires 3 labor-hours. Formulate this nonlinear production planning problem to determine how many FX and ZX skateboards should be produced per week at Scooter's.

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Question 2

Correct Answer:

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FX = number of FX skateboards to produce per week
ZX = number of ZX skateboards to produce per week
Max
5FX -0.2FX ² + 7ZX - 0.3ZX ²
s.t.2FX + 3ZX $\le$ 80
FX, ZX $\ge$ 0

Accepted Answer

FX = number of FX skateboards to produce per week ZX = number of ZX skateboards to produce per week Max 5FX -0.2FX ² + 7ZX - 0.3ZX ² s.t.2FX + 3ZX $\le$ 80 FX, ZX $\ge$ 0

Question 3

Nonlinear programming algorithms are more complex than linear programming algorithms.

Accepted Answer

A) True 
 B)False  True

Question 4

The measure of risk most often associated with the Markowitz portfolio model is the

Accepted Answer

A) portfolio average return. 
B) portfolio minimum return. 
C) portfolio variance. 
D) portfolio standard deviation. 
A) portfolio average return. 
B) portfolio minimum return. 
C) portfolio variance. 
D) portfolio standard deviation.

Question 5

The interpretation of the dual price for nonlinear models is different than the interpretation of the dual price for linear models.

Accepted Answer

A) True 
 B)False

Question 6

Provide several examples of both nonlinear objective functions and nonlinear constraints.

Accepted Answer

Nonlinear objective functions and constr

Question 7

When the number of blending components exceeds the number of storage facilities, the number of feasible solutions to the blending problem

Accepted Answer

A) is reduced. 
B) is increased. 
C) is unchanged. 
D) is zero. 
A) is reduced. 
B) is increased. 
C) is unchanged. 
D) is zero.

Question 8

For a minimization problem, a point is a global minimum if there are no other feasible points with a smaller objective function value.

Accepted Answer

A) True 
 B)False

Question 9

Cutting Edge Yard Care is a residential and commercial lawn service company that has been in business in the Atlanta metropolitan area for almost one year. Cutting Edge would like to use its Atlanta service subscription data below to develop a model for forecasting service subscriptions in other metropolitan areas where it might expand. The first step is to estimate values for p (coefficient of innovation) and q (coefficient of imitation). Formulate the appropriate nonlinear program. $$\begin{array} { c c c } 
\text { Month } & \text { Subscribers } S _ { t } & \text { Cum. Subscribers } C _ { t } \
1 & 0.53 & 0.53 \
2 & 2.04 & 2.57 \
3 & 3.37 & 5.94 \
4 & 4.85 & 10.79 \
5 & 5.14 & 15.93 \
6 & 3.90 & 19.83 \
7 & 2.26 & 22.09 \
8 & 1.43 & 23.52 \
9 & 0.98 & 24.50 \
10 & 0.42 & 24.92
\end{array}$$

Accepted Answer

The answer of Cutting Edge Yard Care is a residential...

Question 10

There are nonlinear applications in which there is a single local optimal solution that is also the global optimal solution.

Accepted Answer

A) True 
 B)False

Question 11

Native Customs sells two popular styles of hand-sewn footwear: a sandal and a moccasin. The cost to make a pair of sandals is $18, and the cost to make a pair of moccasins is $24. The demand for these two items is sensitive to the price, and historical data indicate that the monthly demands are given by S = 400 -10P1 and M = 450 - 15P2 , where S = demand for sandals (in pairs), M = demand for moccasins (in pairs), P1 = price for a pair of sandals, and P2 = price for a pair of moccasins. To remain competitive, Native Customs must limit the price (per pair) to no more than $60 and $75 for its sandals and moccasins, respectively. Formulate this nonlinear programming problem to find the optimal production quantities and prices for sandals and moccasins that maximize total monthly profit.

Accepted Answer

Max 22S - 1/10S ² + 6

Question 12

An investor can pick the mean-variance tradeoff that he or she is most comfortable with by looking at a graph of the

Accepted Answer

A) feasible region. 
B) pooled components. 
C) rolling horizon. 
D) efficient frontier. 
A) feasible region. 
B) pooled components. 
C) rolling horizon. 
D) efficient frontier.

Question 13

Pacific-Gulf Oil Company is faced with the problem of refining three petroleum components into regular and premium gasoline in order to maximize profit. Components 1 and 2 are pooled in a single storage tank and component 3 has its own storage tank. Regular and premium gasolines are made from blending the pooled components and component 3. Prices per gallon for the two products and three components, as well as product specifications, are listed below. $$\begin{array} { l c } 
& \text { Price Per Gallon } \
\text { Regular gasoline } & \$ 2.80 \
\text { Fremium gasoline } & 3.10 \
\text { Component 1 } & 2.40 \
\text { Component 2 } & 2.50 \
\text { Component 3 } & 2.75
\end{array}$$ $$\begin{array} { c c } 
 \text { Product }  & \text { Specifications } \
 \text { Regular gasoline }& \text { At most } 25 \% \text { component } 1 \
& \text { At least } 40 \% \text { component } 2 \
 & \text { At most 30\% component 3 } \
\text { Premium gasoline }& \text { At least 30\% component 1 } \
& \text { At most } 50 \% \text { component 2 } \
& \text { At least } 25 \% \text { component 3 }
\end{array}$$ The maximum number of gallons available for each of the three components is 4000, 8000, and 8000, respectively. Formulate a nonlinear program to determine: 1) what percentages of component 1 and component 2 should be used in the pooled mixture, and 2) how to make regular and premium gasoline by blending the mixture of components 1 and 2 from the pooling tank with component 3.

Accepted Answer

y₁ = gallons of component 1 in the poolin

Question 14

Shampooch is a mobile dog grooming service firm that has been quite successful developing a client base in the Dallas area. The firm plans to expand to other cities in Texas during the next few years. Shampooch would like to use its Dallas subscription data shown below to develop a model for forecasting service subscriptions in cities where it might expand. The first step is to estimate values for p (coefficient of innovation) and q (coefficient of imitation). Formulate the appropriate nonlinear program. $$\begin{array} { c c c } 
\text { Month } & \text { Subscribers St } & \text { Cum. Subscribers } C _ { t } \
1 & 0.42 & 0.42 \
2 & 2.56 & 2.98 \
3 & 3.81 & 6.79 \
4 & 4.47 & 11.26 \
5 & 3.54 & 14.80 \
6 & 2.61 & 17.41 \
7 & 1.90 & 19.31 \
8 & 0.83 & 20.14 \
9 & 0.59 & 20.73
\end{array}$$

Accepted Answer

The answer of Shampooch is a mobile dog grooming service...

Question 15

Describe how the Markowitz portfolio model can be modified to account for upper and lower bounds being placed on the amount of an asset type invested in the portfolio.

Accepted Answer

The Markowitz portfolio model can be mod

Question 16

Which of the following is incorrect?

Accepted Answer

A) A global optimum is a local optimum in a nonlinear optimization problem. 
B) A local maximum is a global maximum in a concave nonlinear optimization problem. 
C) A global minimum is a local minimum in a convex nonlinear optimization problem. 
D) A local optimum is a global optimum in a nonlinear optimization problem. 
A) A global optimum is a local optimum in a nonlinear optimization problem. 
B) A local maximum is a global maximum in a concave nonlinear optimization problem. 
C) A global minimum is a local minimum in a convex nonlinear optimization problem. 
D) A local optimum is a global optimum in a nonlinear optimization problem.

Question 17

In the case of functions with multiple local optima, most nonlinear optimization software methods can get stuck and terminate at a local optimum.

Accepted Answer

A) True 
 B)False

Question 18

In the Bass model for forecasting the adoption of a new product, the objective function

Accepted Answer

A) minimizes the sum of forecast errors. 
B) minimizes the sum of squared forecast errors. 
C) maximizes the number of adoptions. 
D) maximizes the number of adoptions and imitations. 
A) minimizes the sum of forecast errors. 
B) minimizes the sum of squared forecast errors. 
C) maximizes the number of adoptions. 
D) maximizes the number of adoptions and imitations.

Question 19

Because most nonlinear optimization codes will terminate with a local optimum, the solution returned by the codes will be the best solution.

Accepted Answer

A) True 
 B)False

Question 20

The key idea behind constructing an index fund is to choose a portfolio of securities that

Accepted Answer

A) is a mix of growth-oriented and income-oriented stocks. 
B) minimizes risk without sacrificing liquidity. 
C) mimics the performance of a broad market index. 
D) balances short-term and long-term investments. 
A) is a mix of growth-oriented and income-oriented stocks. 
B) minimizes risk without sacrificing liquidity. 
C) mimics the performance of a broad market index. 
D) balances short-term and long-term investments.

If the coefficient of each squared term in a quadratic function is positive, the function is

Nonlinear programming algorithms are more complex than linear programming algorithms.

The measure of risk most often associated with the Markowitz portfolio model is the

The interpretation of the dual price for nonlinear models is different than the interpretation of the dual price for linear models.

Provide several examples of both nonlinear objective functions and nonlinear constraints.

When the number of blending components exceeds the number of storage facilities, the number of feasible solutions to the blending problem

For a minimization problem, a point is a global minimum if there are no other feasible points with a smaller objective function value.

There are nonlinear applications in which there is a single local optimal solution that is also the global optimal solution.

An investor can pick the mean-variance tradeoff that he or she is most comfortable with by looking at a graph of the

Describe how the Markowitz portfolio model can be modified to account for upper and lower bounds being placed on the amount of an asset type invested in the portfolio.

Which of the following is incorrect?

In the case of functions with multiple local optima, most nonlinear optimization software methods can get stuck and terminate at a local optimum.

In the Bass model for forecasting the adoption of a new product, the objective function

Because most nonlinear optimization codes will terminate with a local optimum, the solution returned by the codes will be the best solution.

The key idea behind constructing an index fund is to choose a portfolio of securities that

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance and Operations Management

Advanced Linear Programming Applications

Distribution and Network Problems

Integer Linear Programming

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Exam 8: Nonlinear Optimization Models

If the coefficient of each squared term in a quadratic function is positive, the function is

Nonlinear programming algorithms are more complex than linear programming algorithms.

The measure of risk most often associated with the Markowitz portfolio model is the

The interpretation of the dual price for nonlinear models is different than the interpretation of the dual price for linear models.

Provide several examples of both nonlinear objective functions and nonlinear constraints.

When the number of blending components exceeds the number of storage facilities, the number of feasible solutions to the blending problem

For a minimization problem, a point is a global minimum if there are no other feasible points with a smaller objective function value.

There are nonlinear applications in which there is a single local optimal solution that is also the global optimal solution.

An investor can pick the mean-variance tradeoff that he or she is most comfortable with by looking at a graph of the

Describe how the Markowitz portfolio model can be modified to account for upper and lower bounds being placed on the amount of an asset type invested in the portfolio.

Which of the following is incorrect?

In the case of functions with multiple local optima, most nonlinear optimization software methods can get stuck and terminate at a local optimum.

In the Bass model for forecasting the adoption of a new product, the objective function

Because most nonlinear optimization codes will terminate with a local optimum, the solution returned by the codes will be the best solution.

The key idea behind constructing an index fund is to choose a portfolio of securities that

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance and Operations Management

Advanced Linear Programming Applications

Distribution and Network Problems

Integer Linear Programming

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters