olymmath

SMO 2003 Problem 2

    Find the maximum value of xyz(1+5x)(4x+3y)(5y+6z)(z+18)\frac{xyz}{(1 + 5x)(4x + 3y)(5y + 6z)(z + 18)} as x,yx, y and zz range over the set of all positive real numbers. Justify your answer.

    Dataset text AI-MO AoPS. Quoted with source.

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