Lagrange's Method of Multipliers/Examples

Examples of Use of Lagrange's Method of Multipliers

Arbitrary Example

Find the maximum $M$ of the function $u: \R^2 \to \R$ defined as:

$\forall \tuple {x, y} \in \R^2: \map u {x, y} = x y$

subject to the constraint:

$\text C: \quad x + y = 1$