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Frame $\backslash ($ A B C D E $\backslash )$ consists of four bars welded together to form a single object. Bar $\backslash ($ C D $\backslash )$ is parallel to the $\backslash ($ x $\backslash )$ axis, bars $\backslash ($ A B $\backslash )$ and $\backslash ($ D E $\backslash )$ are parallel to the $\backslash ($ y $\backslash )$ axis, and bar $\backslash ($ B C $\backslash )$ is parallel to the $\backslash ($ z $\backslash )$ axis. The frame is supported by a ball and socket at point $\backslash ($ A $\backslash ),$ a frictionless surface at $\backslash ($ E $\backslash )$ that lies in the $\backslash ($ x z $\backslash )$ plane, cable $\backslash ($ B F $\backslash ),$ and cable $\backslash ($ E F $\backslash ).$ The frame has negligible weight and supports an object $\backslash ($ G $\backslash )$ with mass $\backslash ($ m$\_\{$G$\}\backslash ).$ The cables have the allowable loads listed below.

Assuming that the other members are sufficiently strong, determine the largest value $\backslash ($ m$\_\{$G$\}\backslash )$ may have.

The largest value $\backslash ($ m$\_\{$G$\}\backslash )$ may have is