Question 1

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  True

Question 2

For a typical nonlinear problem, duals price are relatively insensitive to small changes in right-hand side values.

Accepted Answer

A) True 
 B)False  False

Question 3

A feasible solution is a global optimum if there are no other feasible points with a better objective function value in the feasible region.

Accepted Answer

A) True 
 B)False  True

Question 4

The problem of maximizing a concave quadratic function over a linear constraint set is relatively difficult to solve.

Accepted Answer

A) True 
 B)False

Question 5

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 6

​Describe the difference between a convex function and a concave function and give an example of each.

Accepted Answer

A convex function is a function where th

Question 7

Financial planner Minnie Margin wishes to develop a mutual fund portfolio based on the Markowitz portfolio model. She needs to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the variance of the portfolio is minimized subject to the constraint that the expected return of the portfolio be at least 5%. Formulate the appropriate nonlinear program.
​​

Accepted Answer

IS = proportion of portfolio invested in

Question 8

Many linear programming algorithms such as the simplex method optimize by examining only the extreme points of the feasible region.

Accepted Answer

A) True 
 B)False

Question 9

​Explain how the local minimum, local maximum, local optimum, global minimum, global maximum, and global
optimum relate to one another in nonlinear optimization problems.

Accepted Answer

In nonlinear optimization problems, the

Question 10

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 11

The Markowitz mean-variance portfolio model presented in the text is a convex optimization problem.

Accepted Answer

A) True 
 B)False

Question 12

​Explain how the parameters required for the Bass new-product adoption model can be estimated when no historical
data are available for the new product.

Accepted Answer

When historical data for a new product a

Question 13

When components (or ingredients) in a blending problem must be pooled, the number of feasible solutions is reduced.

Accepted Answer

A) True 
 B)False

Question 14

It is possible for the optimal solution to a nonlinear optimization problem to lie in the interior of the feasible region.

Accepted Answer

A) True 
 B)False

Question 15

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.

Accepted Answer

Min E₁² + E₂² + E₃² + E₄² + E₅² + E₆² + E₇² + E₈² + E₉² F₁

Question 16

A function is quadratic if its nonlinear terms have a power of 4.

Accepted Answer

A) True 
 B)False

Question 17

Financial planner Minnie Margin has a substantial number of clients who wish to own a mutual fund portfolio that matches, as a whole, the performance of the Russell 2000 index. Her task is to determine what proportion of the portfolio should be invested in each of the five mutual funds listed below so that the portfolio most closely mimics the performance of the Russell 2000 index. Formulate the appropriate nonlinear program.
​   ​

Accepted Answer

IS = proportion of portfolio invested in

Question 18

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 19

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 /10 S ² +

Question 20

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.

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

For a typical nonlinear problem, duals price are relatively insensitive to small changes in right-hand side values.

A feasible solution is a global optimum if there are no other feasible points with a better objective function value in the feasible region.

The problem of maximizing a concave quadratic function over a linear constraint set is relatively difficult to solve.

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

Describe the difference between a convex function and a concave function and give an example of each.

Many linear programming algorithms such as the simplex method optimize by examining only the extreme points of the feasible region.

Explain how the local minimum, local maximum, local optimum, global minimum, global maximum, and global optimum relate to one another in nonlinear optimization problems.

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

The Markowitz mean-variance portfolio model presented in the text is a convex optimization problem.

Explain how the parameters required for the Bass new-product adoption model can be estimated when no historical data are available for the new product.

When components (or ingredients) in a blending problem must be pooled, the number of feasible solutions is reduced.

It is possible for the optimal solution to a nonlinear optimization problem to lie in the interior of the feasible region.

A function is quadratic if its nonlinear terms have a power of 4.

Which of the following is incorrect?

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

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 Models

Integer Linear Programming

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and 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

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

For a typical nonlinear problem, duals price are relatively insensitive to small changes in right-hand side values.

A feasible solution is a global optimum if there are no other feasible points with a better objective function value in the feasible region.

The problem of maximizing a concave quadratic function over a linear constraint set is relatively difficult to solve.

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

​Describe the difference between a convex function and a concave function and give an example of each.

Many linear programming algorithms such as the simplex method optimize by examining only the extreme points of the feasible region.

​Explain how the local minimum, local maximum, local optimum, global minimum, global maximum, and global optimum relate to one another in nonlinear optimization problems.

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

The Markowitz mean-variance portfolio model presented in the text is a convex optimization problem.

​Explain how the parameters required for the Bass new-product adoption model can be estimated when no historical data are available for the new product.

When components (or ingredients) in a blending problem must be pooled, the number of feasible solutions is reduced.

It is possible for the optimal solution to a nonlinear optimization problem to lie in the interior of the feasible region.

A function is quadratic if its nonlinear terms have a power of 4.

Which of the following is incorrect?

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

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 Models

Integer Linear Programming

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and 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

Describe the difference between a convex function and a concave function and give an example of each.

Explain how the local minimum, local maximum, local optimum, global minimum, global maximum, and global optimum relate to one another in nonlinear optimization problems.

Explain how the parameters required for the Bass new-product adoption model can be estimated when no historical data are available for the new product.