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I would appreciate if somebody could help me with the following problem:

Find the maximum of the function $$f(a,b,c)=\frac{a}{1+b+c}+ \frac{b}{1+c+a}+ \frac{c}{1+a+b}+(1-a)(1-b)(1-c)~~(0\leq a,b,c\leq1) $$

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if you don't mind using calculus, maybe you could try the method of Lagrange multipliers? en.wikipedia.org/wiki/Lagrange_multiplier –  Enzo Feb 15 '13 at 14:33

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Value to Function at 0.5 will be the maximum value which is 2.25. :)

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I'm sure it's right, but I think a brief explanation wouldn't harm. –  AndreasT Feb 15 '13 at 10:26

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