Consider the following network of Hawaii Island, which shows the location of various facilities within a youth camp and the distances $($in tens of yards$)$ between each facility. Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp $($and to minimize the construction time and cost$),$ the directors want to determine which paths should be constructed. Use this network to determine which paths should be built to connect all facilities with the minimum distance.