Question 1

Given the nonlinear programming model Max Z = 5x1 - 2x1- 3x22
Subject to: x1 + 4x2 = 6
What is the Lagrangian function?

Accepted Answer

5x₁ - 2x₂+-3x₂²- λ (x₁+4x₂ - 6)

Question 2

The Lagrange multiplier is ________ the dual variables in a linear programming problem.

Accepted Answer

A)  analogous to 
B)  contradictory to 
C)  inversely related to 
D)  the opposite of 
A)  analogous to 
B)  contradictory to 
C)  inversely related to 
D)  the opposite of A

Question 3

The slope of a curve at any point is equal to the derivative of the curves function.

Accepted Answer

A) True 
 B)False  True

Question 4

The method of Lagrange multipliers can only be used in solving nonlinear programming problems with one equality constraint.

Accepted Answer

A) True 
 B)False

Question 5

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

Accepted Answer

A)  in the order of the variables. 
B)  one after the other. 
C)  one at a time. 
D)  simultaneously. 
A)  in the order of the variables. 
B)  one after the other. 
C)  one at a time. 
D)  simultaneously.

Question 6

The derivative of a function equals the slope of the curve defined by that function.

Accepted Answer

A) True 
 B)False

Question 7

The Lagrange multiplier reflects the appropriate change in the objective function resulting from a unit change in the quantity value of the constraint equation.

Accepted Answer

A) True 
 B)False

Question 8

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

Accepted Answer

The answer of Given the nonlinear programming model  Max...

Question 9

The Lagrange multiplier, λ, reflects a change in the objective function from a unit change in the ________ value of a constraint.

Accepted Answer

The answer of The Lagrange multiplier, λ, reflects a change...

Question 10

A customer molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The per unit contribution for the juice glasses (x1) is equal to 60 - 5x1, and the per unit contribution for the cocktail glasses (x2) is 80 - 4x2 for a total contribution of 60x1 - 5x12 + 80x2- 4x22. Demand requires that the production of juice glasses is twice the production of cocktail glasses.(x1 = 2x2). What is the Lagrangian function for this problem?

Accepted Answer

L = 60x1 -

Question 11

If a nonlinear programming problem results in profit (Z) of $250, and the Lagrange multiplier for a constraint is 5, the new profit will be ________ if the right-hand side of the constraint is decreased by 1 unit.

Accepted Answer

The answer of If a nonlinear programming problem results in...

Question 12

The slope of a curve at its highest point equals 1.

Accepted Answer

A) True 
 B)False

Question 13

The slope of a curve at its highest point equals:

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  3 
A)  0 
B)  1 
C)  2 
D)  3

Question 14

A customer molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The per unit contribution for the juice glasses (x1) is equal to 60 - 5x1, and the per unit contribution for the cocktail glasses (x2) is 80 - 4 x2 for a total contribution of 60x1 - 5x12 + 80x2 - 4x22. Demand requires that the production of juice glasses is twice the production of cocktail glasses (x1 = 2x2). Write the objective function for this problem which illustrates the technique of substitution.

Accepted Answer

20x₂ - 24

Question 15

The Lagrangian function is the original objective function plus the Lagrange multiplier times the difference of the left and right sides of the constraint.

Accepted Answer

A) True 
 B)False

Question 16

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

The answer of Given the nonlinear programming model Max Z...

Question 17

If total contribution of is expressed as C = 60x1 - 5x12 + 80x2 - 4x22 and x1 = 2x2, then the Lagrangian function is 60x1 - 5x12 + 80x2 - 4x22 ________.

Accepted Answer

-? (x<sub>

Question 18

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

Accepted Answer

A) True 
 B)False

Question 19

The Lagrange multiplier reflects the appropriate change in the objective function resulting from a unit change in the ________ of the constraint equation.

Accepted Answer

A)  coefficient 
B)  objective function 
C)  right-hand side 
D)  shadow price 
A)  coefficient 
B)  objective function 
C)  right-hand side 
D)  shadow price

Question 20

In the method of ________, constraints as multiples of multiplier λ are subtracted from the objective function, which is then differentiated with respect to each variable and solved.

Accepted Answer

Lagrange m

Given the nonlinear programming model Max Z = 5x₁ - 2x₁- 3x₂² Subject to: x₁ + 4x₂ = 6 What is the Lagrangian function?

The Lagrange multiplier is ________ the dual variables in a linear programming problem.

The slope of a curve at any point is equal to the derivative of the curves function.

The method of Lagrange multipliers can only be used in solving nonlinear programming problems with one equality constraint.

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

The derivative of a function equals the slope of the curve defined by that function.

The Lagrange multiplier reflects the appropriate change in the objective function resulting from a unit change in the quantity value of the constraint equation.

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

The Lagrange multiplier, λ, reflects a change in the objective function from a unit change in the ________ value of a constraint.

If a nonlinear programming problem results in profit (Z) of $250, and the Lagrange multiplier for a constraint is 5, the new profit will be ________ if the right-hand side of the constraint is decreased by 1 unit.

The slope of a curve at its highest point equals 1.

The slope of a curve at its highest point equals:

The Lagrangian function is the original objective function plus the Lagrange multiplier times the difference of the left and right sides of the constraint.

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

If total contribution of is expressed as C = 60x₁ - 5x₁² + 80x₂ - 4x₂² and x₁ = 2x₂, then the Lagrangian function is 60x₁ - 5x₁² + 80x₂ - 4x₂² ________.

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

The Lagrange multiplier reflects the appropriate change in the objective function resulting from a unit change in the ________ of the constraint equation.

In the method of ________, constraints as multiples of multiplier λ are subtracted from the objective function, which is then differentiated with respect to each variable and solved.

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

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Exam 20: Nonlinear Programming: Solution Techniques

Given the nonlinear programming model Max Z = 5x1 - 2x1- 3x22 Subject to: x1 + 4x2 = 6 What is the Lagrangian function?

The Lagrange multiplier is ________ the dual variables in a linear programming problem.

The slope of a curve at any point is equal to the derivative of the curves function.

The method of Lagrange multipliers can only be used in solving nonlinear programming problems with one equality constraint.

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

The derivative of a function equals the slope of the curve defined by that function.

The Lagrange multiplier reflects the appropriate change in the objective function resulting from a unit change in the quantity value of the constraint equation.

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

The Lagrange multiplier, λ, reflects a change in the objective function from a unit change in the ________ value of a constraint.

If a nonlinear programming problem results in profit (Z) of $250, and the Lagrange multiplier for a constraint is 5, the new profit will be ________ if the right-hand side of the constraint is decreased by 1 unit.

The slope of a curve at its highest point equals 1.

The slope of a curve at its highest point equals:

The Lagrangian function is the original objective function plus the Lagrange multiplier times the difference of the left and right sides of the constraint.

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

If total contribution of is expressed as C = 60x1 - 5x12 + 80x2 - 4x22 and x1 = 2x2, then the Lagrangian function is 60x1 - 5x12 + 80x2 - 4x22 ________.

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

The Lagrange multiplier reflects the appropriate change in the objective function resulting from a unit change in the ________ of the constraint equation.

In the method of ________, constraints as multiples of multiplier λ are subtracted from the objective function, which is then differentiated with respect to each variable and solved.

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

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Given the nonlinear programming model Max Z = 5x₁ - 2x₁- 3x₂² Subject to: x₁ + 4x₂ = 6 What is the Lagrangian function?

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

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

If total contribution of is expressed as C = 60x₁ - 5x₁² + 80x₂ - 4x₂² and x₁ = 2x₂, then the Lagrangian function is 60x₁ - 5x₁² + 80x₂ - 4x₂² ________.