How do you do? - 2

Algebra Level 5

\[ I = xyz \\ J = xy^2 z \\ K = xyz^3 \]

Find the sum of the maximum values of the expression \(I\), \(J\), and \(K\) if positive reals \(x,y,z\) are constrained by \(2x + 3y + 4z = 60\).

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