Consider a network given in the figure below, where dotted lines between nodes represent potential links that can be selected in order to connect nodes.

$($i$)$ If we want to connect all the nodes, find an optimal solution to minimize the total length of selected links. $(5$ points$)$

$($ii$)$ Suppose that we have a constraint that at most one of the $3$ links $-$ AD$,$ CD$,$ and ABcan be included. Then find just next solution of Tabu search algorithm by using the solution obtained $($i$)$ as the current solution. $(10$ points$)$