subject
to one or more equality constraints
The
solution is found by minimizing
with
respect to the
and
The
Lagrange multipliers are the
University Maths Notes: Calculus – 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 maximise
subject
to
form
the expression
Differentiating with respect to
gives
(1)
Differentiating with respect to
gives
(2)
Differentiating with respect to
gives
(3)
From (1)
From (2)
From (3)
The maximum value of
is
then
This is illustrated below. The maximum is where the curves touch.
