Let $x,y,z>0$ and satisfying $3xy+yz+2zx=6$
Find Maximum of this expression: $P=\frac{1}{x^2+1}+\frac{4}{y^2+4}+\frac{3z}{9+z^2}$
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Have you tried using Lagrange Multipliers? – JimmyK4542 Jun 19 '14 at 21:44
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Generically, this is a duplicate of this and this, which both use Lagrange multipliers. I'm closing this question as an abstract duplicate. – davidlowryduda Nov 26 '15 at 03:45