Q:

Number of Lagrange Multipliers

Suppose we are looking at the following:
$$ \text{minimize} \ f(x) = x^2+y^2 \\ \text{subject to} \ \  x+y-2 \geq 0$$
Would there only be one Lagrange multiplier corresponding to the single constraint? Or would there be two Lagrange multipliers corresponding to $x$ and $y$?

A:

The number of Lagrange multipliers only depends on the number of constraints you have and not on the number of unknowns. For this problem, you can get the solution graphically as shown below.

