Before revision:  When the number of masses is two we find the optimal load analytically. For the case of three or more masses, we obtain conjectures for the globally optimal load that are strongly supported by extensive computational results .
After revision:  The stability constraint is nonconvex and nonsmooth, making the optimization problem quite challenging. We give a detailed analytical treatment for the case of three or more masses, we obtain conjectures for the globally optimal load that are strongly supported by extensive computational results .