Bounds or no bounds?

Algebra Level pending

Find the maximum value of \((1-x)(2-y)(3-z)(x+\frac{y}{2}+\frac{z}{3})\), where \(1<x, 2<y, 3<z\) and \(x+\frac{y}{2}+\frac{z}{3}>0\).

NOTE: Round off your answer to 4 decimal places.

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