## Lagrange Multipliers

Lagrange multipliers are used in optimising or maximising a functionsubject to one or more equality constraintsThe solution is found by minimizingwith respect to theandThe Lagrange multipliers are the

For example to maximisesubject toform the expression

Differentiating with respect togives (1)

Differentiating with respect togives (2)

Differentiating with respect togives (3)

From (1)

From (2)

From (3)

The maximum value ofis then

This is illustrated below. The maximum is where the curves touch.