Three factories 1, 2, 3 are each supplied underground by water, gas, and electricity, from poins A, B, C respectively. Show that this can be represented by K3,3 (the complete bipartite graph G = (S, T; E) with S and T consisting of three vertices each) and that eight of the nine supply lines (edges) can be laid out without crossing. Make it plausible that K3,3 is not planar by attempting to draw the ninth line without crossing the others.