Question 1

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 2

The slope of a curve at its highest point equals:
A) 0
B) 1
C) 2
D) 3

Accepted Answer

At the highest point of a curve or a function, the slope of the curve is equal to 0. This is because, at the highest point or the peak, the function changes direction from increasing to decreasing or vice versa, and the slope or the derivative of the function is zero at this point. Therefore, the correct answer is A) 0.

Question 3

In solving a maximization problem, the optimal profit associated with the relaxed solution is always less than or equal to the value of the optimal profit associated with the ________ solution.

Accepted Answer

The answer of In solving a maximization problem, the optimal...

Question 4

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

The answer of A customer molder produces 6-ounce juice glasses...

Question 5

Given the nonlinear programming model Max Z = 4x₁ - 0.1x₁x₂ + 5x₂ - 0.2 x₂² Subject to: x₁ + 2x₂ = 4 What is the Lagrangian function?

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

The answer of A customer molder produces 6-ounce juice glasses...

Question 8

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

Accepted Answer

The answer of Write the Lagrangian function for the following...

Question 9

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 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

The answer of If the substitution method cannot be used...

Question 11

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 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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 15

Solve the following nonlinear program: Min x1² + 2x₂² - 8x₁ - 12x₂ + 34 subject to: x₁² + 2x₂² = 5

Accepted Answer

The answer of Solve the following nonlinear program: Min x1² +...

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

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

Question 17

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

Accepted Answer

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

Question 18

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 19

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

Accepted Answer

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

Question 20

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

The answer of If total contribution of is expressed as...

Quiz 20: Nonlinear Programming: Solution Techniques

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:

In solving a maximization problem, the optimal profit associated with the relaxed solution is always less than or equal to the value of the optimal profit associated with the ________ solution.

Given the nonlinear programming model Max Z = 4x1 - 0.1x1x2 + 5x2 - 0.2 x22 Subject to: x1 + 2x2 = 4 What is the Lagrangian function?

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

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

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

Given the nonlinear programming model Max Z = 5x1 - 2x22 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?

Solve the following nonlinear program: Min x12 + 2x22 - 8x1 - 12x2 + 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?

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

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

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

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

Given the nonlinear programming model Max Z = 4x₁ - 0.1x₁x₂ + 5x₂ - 0.2 x₂² Subject to: x₁ + 2x₂ = 4 What is the Lagrangian function?

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

Given the nonlinear programming model Max Z = 5x₁ - 2x₂² 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?

Solve the following nonlinear program: Min x1² + 2x₂² - 8x₁ - 12x₂ + 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 - 2x₁- 3x₂² Subject to: x₁ + 4x₂ = 6 What is the Lagrangian function?

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