When asked to apply the Lagrange Multiplier method it is time to pull out your trusty TI89 , open Calculus Made Easy (download www.TI89.com) , go to Multivariable Calculus under F6 3 , there select Lagrange Multiplier under F3 E . Enter Lagrange Multiplier problems as follow
Just leave the box for the 2. constraint empty if it is not given. Press ENTER .
Voila. The solution(s) show immediately. Just scroll right and left to view it in its entirety. You will always get the correct solution this way.