What is a boundary point when solving for a max/min using Lagrange Multipliers? After you solve the required system of equation and get the critical maxima and minima, when do you have to check for boundary points and how do you identify them?
e.g. Optimise (1+a)(1+b)(1+c) given constraint a+b+c=1, with a,b,c all non-negative.
After using the Lagrange multiplier equating the respective partial derivatives, I get (a,b,c)=(1/3, 1/3, 1/3). Clearly there must be both a maximum and minimum, and I assume this is the maximum. Where is the minimum? (0,0,1) optimises best for the minimum, and I assume using 0 is a boundary point but why? And what effect does the restriction to non-negative reals have?