Linear programming lagrange multipliers

1. What is Lagrange's multiplier method?
2. How do you solve Lagrange multiplier problems?
3. What is the advantage of using Lagrange multiplier?
4. When not to use Lagrange multipliers?

What is Lagrange's multiplier method?

Lagrange multiplier method is a technique for finding a maximum or minimum of a function F(x,y,z) subject to a constraint (also called side condition) of the form G(x,y,z) = 0. Figure 1: The four possible cases of varying end points in the direction of y.

How do you solve Lagrange multiplier problems?

A good approach to solving a Lagrange multiplier problem is to first elimi$ nate the Lagrange multiplier # using the two equations fx / #gx and fy / #gy. Then solve for x and y by combining the result with the constraint g ! x, y" / k, thus producing the critical points.

What is the advantage of using Lagrange multiplier?

The Lagrange multiplier method can be used to solve non-linear programming problems with more complex constraint equations and inequality constraints. However the method must be altered to compensate for inequality constraints and is practical for solving only small problems.

When not to use Lagrange multipliers?

Recall that a minimum for a differentiable function occurs either at a point where the derivative is 0, or on the boundary. If the minimum is an interior point, the Lagrange multipliers won't matter.