Consider the following decision problem. Suppose $\backslash ($ n $\backslash )$ groups attend a social event. There are $\backslash ($ m $\backslash )$ tables for serving lunch such that $\backslash ($ m $\backslash$geq n $\backslash ).$ Further suppose group $\backslash ($ i $\backslash )$ has $\backslash ($ x$\_\{$i$\}\backslash )$ members, and table $\backslash ($ i $\backslash )$ has $\backslash ($ y$\_\{$i$\}\backslash )$ chairs. We wish to arrange a sitting so that no two members of the same team sit at the same table $($to maximize socializing$).$ Is it possible to make such an arrangement? Specify whether the above decision problem can be solved in polynomial time or not. Justify your answer.