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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 be the corresponding altitudes of the tetrahedron. If 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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