MathDB

4

Part of 2006 Baltic Way

Problems(1)

Maximal value when a+b+c+d+e+f=6

Source: Baltic Way 2006

12/4/2010
Let a,b,c,d,e,fa,b,c,d,e,f be non-negative real numbers satisfying a+b+c+d+e+f=6a+b+c+d+e+f=6. Find the maximal possible value of
\color{white}\ .  \ \color{black}\   abc+bcd+cde+def+efa+fab
and determine all 66-tuples (a,b,c,d,e,f)(a,b,c,d,e,f) for which this maximal value is achieved.
inequalitiesinequalities proposed