Question 1

In the method of Lagrange multipliers, the model constraints are multiplied by Lagrange multipliers and ________ the objective function.

Accepted Answer

A)  divided by 
B)  multiplied by 
C)  added to 
D)  subtracted from 
A)  divided by 
B)  multiplied by 
C)  added to 
D)  subtracted from

Question 2

The Lagrange multiplier reflects a change in the objective function from a unit change in the right-hand-side value of a constraint.

Accepted Answer

A) True 
 B)False

Question 3

The Lagrangian function is differentiated with respect to each variable, and the resulting equations are solved simultaneously.

Accepted Answer

A) True 
 B)False

Question 4

Given the nonlinear programming model:
Max Z = 5x1 - 2x22
Subject to: x1 + x2 = 6
What is the optimal value of the Lagrange multiplier?

Accepted Answer

A)  λ = 1 
B)  λ = 2 
C)  λ = 3 
D)  λ = 4 
E)  λ = 5 
A)  λ = 1 
B)  λ = 2 
C)  λ = 3 
D)  λ = 4 
E)  λ = 5

Question 5

Given the nonlinear programming model:
Max Z = 5x1 - 2x22
Subject to: x1 + x2 = 6
What is the optimal value of the objective function?

Accepted Answer

A)  Z = 19.625 
B)  Z = 20.625 
C)  Z = 21.625 
D)  Z = 22.625 
E)  Z =23.625 
A)  Z = 19.625 
B)  Z = 20.625 
C)  Z = 21.625 
D)  Z = 22.625 
E)  Z =23.625

Question 6

The Lagrangian function is differentiated with respect to each variable and the resulting equations are solved ________ to obtain the value of each variable.

Accepted Answer

The answer of The Lagrangian function is differentiated with respect...

Question 7

Linear programming is a special case of nonlinear programming.

Accepted Answer

A) True 
 B)False

Question 8

Write the Lagrangian function for the following nonlinear program:
Min x12+ 2x22 - 8x1 - 12x1 + 34
subject to: x12 + 2x22 = 5

Accepted Answer

L = x12 + 2x22 - 8x1

Question 9

A store has determined that the weekly sales of a product is related to the number of customers who visit the store and the square feet of shelf space, x, according to the following equation: -20x2 - 10C2 + 40Cx + 120x - 200C + 600. C represents the hundreds of customers who visit their store. If a store averages 200 customers per week, which of these methods represents the simplest way to determine the optimal number of square feet of shelf space for the product?

Accepted Answer

A)  Lagrangian functions 
B)  Excel Solver 
C)  substitution method 
D)  solution of simultaneous equations 
E)  none of the above 
A)  Lagrangian functions 
B)  Excel Solver 
C)  substitution method 
D)  solution of simultaneous equations 
E)  none of the above

Question 10

If the substitution method cannot be used to solve a nonlinear problem, then the equations which result from taking partial derivatives must be solved using the method of ________.

Accepted Answer

simultaneo

Question 11

The Lagrangian function is ________ with respect to each variable and the resulting equations are solved simultaneously.

Accepted Answer

The answer of The Lagrangian function is ________ with respect...

Question 12

In the substitution method, the constraint equation is solved for one variable ________ and then substituted into the objective function.

Accepted Answer

A)  only 
B)  after another 
C)  at a time 
D)  in terms of another 
A)  only 
B)  after another 
C)  at a time 
D)  in terms of another

Question 13

The slope of a curve at its highest point equals ________.

Accepted Answer

The answer of The slope of a curve at its...

Question 14

The least complex method for solving nonlinear programming problems is referred to as

Accepted Answer

A)  the substitution method. 
B)  Lagrange multipliers. 
C)  nonlinear programming. 
D)  none of the above 
A)  the substitution method. 
B)  Lagrange multipliers. 
C)  nonlinear programming. 
D)  none of the above

Question 15

Given the nonlinear programming model:
Max Z = 5x1 - 2x22
Subject to: x1 + x2 = 6
What are the optimal values of x1 and x2?

Accepted Answer

A)  x1 = 4.75, x2 = 1.25 
B)  x1 = 5.00, x2 = 3.25 
C)  x1 = 4.50, x2 = 2.25 
D)  x1 = 4.50, x2 = 1.25 
E)  x1 = 5.75, x2 = 0.75 
A)  x1 = 4.75, x2 = 1.25 
B)  x1 = 5.00, x2 = 3.25 
C)  x1 = 4.50, x2 = 2.25 
D)  x1 = 4.50, x2 = 1.25 
E)  x1 = 5.75, x2 = 0.75

Question 16

Given the nonlinear programming model Max Z = 5x1 - 2x22
Subject to: x1 + x2 = 6
What are the optimal values of x1 and x2?

Accepted Answer

x1 = 4.75,

Question 17

If a Lagrange multiplier equals 3, a one-unit increase in the right-hand side of a constraint, will result in an increase of 3 in the objective function.

Accepted Answer

A) True 
 B)False

Question 18

Solving nonlinear optimization problems using Lagrange multipliers requires

Accepted Answer

A)  calculus. 
B)  algebra. 
C)  computers. 
D)  A and B 
E)  A and C 
A)  calculus. 
B)  algebra. 
C)  computers. 
D)  A and B 
E)  A and C

Question 19

The slope of a curve at its highest point equals 0.

Accepted Answer

A) True 
 B)False

Question 20

The ________ method for solving nonlinear programming problems is referred to as substitution.

Accepted Answer

A)  least complex 
B)  most complex 
C)  most difficult 
D)  least difficult 
A)  least complex 
B)  most complex 
C)  most difficult 
D)  least difficult

Exam 20: Nonlinear Programming: Solution Techniques

In the method of Lagrange multipliers, the model constraints are multiplied by Lagrange multipliers and ________ the objective function.

The Lagrange multiplier reflects a change in the objective function from a unit change in the right-hand-side value of a constraint.

The Lagrangian function is differentiated with respect to each variable, and the resulting equations are solved simultaneously.

Given the nonlinear programming model: Max Z = 5x1 - 2x22 Subject to: x1 + x2 = 6 What is the optimal value of the Lagrange multiplier?

Given the nonlinear programming model: Max Z = 5x1 - 2x22 Subject to: x1 + x2 = 6 What is the optimal value of the objective function?

The Lagrangian function is differentiated with respect to each variable and the resulting equations are solved ________ to obtain the value of each variable.

Linear programming is a special case of nonlinear programming.

Write the Lagrangian function for the following nonlinear program: Min x12+ 2x22 - 8x1 - 12x1 + 34 subject to: x12 + 2x22 = 5

If the substitution method cannot be used to solve a nonlinear problem, then the equations which result from taking partial derivatives must be solved using the method of ________.

The Lagrangian function is ________ with respect to each variable and the resulting equations are solved simultaneously.

In the substitution method, the constraint equation is solved for one variable ________ and then substituted into the objective function.

The slope of a curve at its highest point equals ________.

The least complex method for solving nonlinear programming problems is referred to as

Given the nonlinear programming model: Max Z = 5x1 - 2x22 Subject to: x1 + x2 = 6 What are the optimal values of x1 and x2?

Given the nonlinear programming model Max Z = 5x1 - 2x22 Subject to: x1 + x2 = 6 What are the optimal values of x1 and x2?

If a Lagrange multiplier equals 3, a one-unit increase in the right-hand side of a constraint, will result in an increase of 3 in the objective function.

Solving nonlinear optimization problems using Lagrange multipliers requires

The slope of a curve at its highest point equals 0.

The ________ method for solving nonlinear programming problems is referred to as substitution.

Management Science

Linear Programming: Model Formulation and Graphical Solution

Linear Programming: Computer Solution and Sensitivity Analysis

Linear Programming: Modeling Examples

Integer Programming

Transportation, Transshipment, and Assignment Problems

Network Flow Models

Project Management

Multicriteria Decision Making

Nonlinear Programming

Probability and Statistics

Decision Analysis

Queuing Analysis

Simulation

Forecasting

Inventory Management

the Simplex Solution Method

Transportation and Assignment Solution Methods

Integer Programming: the Branch and Bound Method

Game Theory

Markov Analysis

Filters

Given the nonlinear programming model: Max Z = 5x₁ - 2x₂² Subject to: x₁ + x₂ = 6 What is the optimal value of the Lagrange multiplier?

Given the nonlinear programming model: Max Z = 5x₁ - 2x₂² Subject to: x₁ + x₂ = 6 What is the optimal value of the objective function?

Write the Lagrangian function for the following nonlinear program: Min x1²+ 2x₂² - 8x₁ - 12x₁ + 34 subject to: x1² + 2x₂² = 5

Given the nonlinear programming model: Max Z = 5x₁ - 2x₂² Subject to: x₁ + x₂ = 6 What are the optimal values of x1 and x2?

Given the nonlinear programming model Max Z = 5x₁ - 2x₂² Subject to: x₁ + x₂ = 6 What are the optimal values of x₁ and x₂?