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CN-LEAGUE 2017 Problem 10

    Let x1,x2,x3≥0x_1,x_2,x_3\geq 0 and x1+x2+x3=1x_1+x_2+x_3=1 . Find the minimum value and the maximum value of (x1+3x2+5x3)(x1+x23+x35).(x_1+3x_2+5x_3)\left(x_1+\frac{x_2}{3}+\frac{x_3}{5}\right).

    Dataset text AI-MO AoPS. Quoted with source.

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