$1)$ The system consists of cables $\backslash ($ A B$,$ B C$,$ C D $\backslash ),$ and $\backslash ($ C E $\backslash ).$ If the cables have failure strength shown in the table, find the largest weight $\backslash (($W$)\backslash )$ that can be supported by the system.

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|\}$

$\backslash$hline member & strength $\backslash \backslash$

$\backslash$hline$\backslash ($ A B $\backslash )$ & $200$ lb $\backslash \backslash$

$\backslash$hline$\backslash ($ B C $\backslash )$ & $400$ lb $\backslash \backslash$

$\backslash$hline$\backslash ($ C D $\backslash )$ & $198$ lb $\backslash \backslash$

$\backslash$hline$\backslash ($ C E $\backslash )$ & $300$ lb $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$