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Let A(1), A(2), A(3), A(4) be the areas ...

Let `A_(1), A_(2), A_(3), A_(4)` be the areas of the triangular faces of a tetrahedron, and `h_(1), h_(2), h_(3), h_(4)` be the corresponding altitudes of the tetrahedron. If the volume of tetrahedron is `1//6` cubic units, then find the minimum value of ` (A_(1) +A_(2) + A_(3) + A_(4))(h_(1)+ h_(2)+h_(3)+h_(4))` (in cubic units).

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