Lagrange FAIL

by v_Enhance, Oct 24, 2010, 11:45 PM

Quote:
Subject to the constraints
$\frac{x}{4}+\frac{y}{4}+\frac{4z}{9}=\frac{m}{3},$
$\frac{x}{2}+\frac{3 y}{8}+\frac{z}{3}=\frac{5m}{12}, $
$ \frac{x}{4}+\frac{3 y}{8}+\frac{2z}{9}=\frac{m}{4},$
$0 \leq x,y,z \leq1$

Maximize $m$.
I spent about an hour attempting to bash this problem with Lagrange and wondering why it kept n giving me the minimum (0,0,0) before I realized I really ought to check the boundary.

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