Minimum Spanning Tree — practice questions

A network has nodes P, Q, R, S, T with arcs $PQ = 7$, $PR = 9$, $QR = 4$, $QS = 6$, $RT = 8$, $ST = 5$, $RS = 11$. Use Kruskal's algorithm to find the minimum spanning tree and its total weight.

A ski field must run power to five huts. The possible cable runs, in hundreds of metres, are $AB = 12$, $AC = 15$, $BC = 9$, $BD = 14$, $CD = 14$, $CE = 20$, $DE = 11$. Cable costs $85 per metre. Find the cheapest way to power all five huts, and explain why one tie in the weights does not affect your answer.

A regional council has already built the link $CD$ (5 km) in the six-station network ($AB = 4$, $AC = 6$, $BC = 3$, $BD = 8$, $CD = 5$, $CE = 11$, $DE = 4$, $DF = 9$, $EF = 3$). It now asks: what is the cheapest way to connect all six stations given that $CD$ is already built, and would the answer change if instead the expensive arc $CE$ had already been built? Justify your reasoning in general terms.