[RESOLVED] An Engineering Math Question

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I have a regular hexagonal platform of uniform density pictured below. The inscribed circle has a radius of 2.75 units. I which to hang six weights 1 through 6 at points A through F in an optimal arrangement of one weight per point. These points are located at the intersection of the inscribed circle and the diagonals that connect the opposite points of the hexagon:



The values of the weights (1 - 6) are shown in the table. First, how should I arrange the weights 1-6 on points A-F so that when the platform is suspended at unknown point X, the hexagon (1) hangs dead flat and (2) the distance OX is minimized.

Second, what is the distance and location of point X relative to O, given the optimal arrangement of the weights?

One other variable, at point O, another weight = 30 exists and is fixed at that center location.