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What is a good way to calculate max/min of $$x_1 x_2+y_1 y_2+z_1 z_2+w_1 w_2$$ where $x_1+y_1+z_1+w_1=a$ and $x_2+y_2+z_2+w_2=b$ and $x, y, z, w, a, b \in \mathbb{N} \cup \{0 \}$, and please explain your answer (how your result comes out).

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    You can solve this by showing that if $c>d$ then $c(e+1)+df>ce+d(f+1)$.2011-05-16
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    henry's hint hits the point i think, but thanks all.2011-05-16

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