Please answer all parts completely and explain your work.

Question 1: The Wirehouse Lumber Company will soon begin logging eight groves of trees in the same general area. Therefore, it must develop a system of dirt roads that makes each grove accessible from every other grove. The distance (in miles) between every pair of groves is as follows: Distance between Pairs of Groves 1 2 3 4 5 6 7 8 1.3 . 2.1 0.9 0.9 1.8 2.6 0.7 1.2 1.7 0.7 1 2 3 4 5 6 7 8 1.3 2.1 0.9 0.7 1.8 2.0 1.5 Grove 1.8 2.6 2.5 1.6 0.9 | 2.0 2.3 1.9 1.5 1.1 0.6 0.9 1.8 1.2 2.6 2.3 1.1 1.5 1.1 1.0 0.9 0.8 1.0 0.5 2.6 1.7 2.5 1.9 1.0 an 0.7 1.6 1.5 0.9 0.9 1.1 0.8 0.6 1.0 0.5 Management now wishes to determine between which pairs of groves the roads should be constructed to connect all groves with a minimum total length of road. (a) Describe how this problem fits the network description of the minimum spanning tree problem. (b) Use the algorithm described in the lecture to solve the