Exam 20: Nonlinear Programming: Solution Techniques

In the ________ method, the constraint equation is solved for one variable in terms of another and then substituted into the objective function.

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

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

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.

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

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

Consider the following objective function and constraint: C(x) = 2x12 - 15x + 3x23 - 9x2 + 30, such that x1 = 3x2. Which of the following is the correct Lagrangian function?

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

The Lagrange multiplier at the optimum gives only the instantaneous rate of change in the objective value.

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

In the substitution method, the constraint equation is solved for one variable in terms of another and then substituted into the objective function.

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

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

Lagrange multiplier is another name for shadow price.

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