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Use the quick (approximate) travelling salesperson construction to find a tour for the cost matrix below. The first node used should be node 1. In

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Use the quick (approximate) travelling salesperson construction to find a tour for the cost matrix below. The first node used should be node 1. In what order are nodes inserted by the algorithm? What is the total cost of the tour produced? I wish to model the following word problem as a graph problem: The Maytag repairman has been called to repair washers and dryers at several customer's homes. Assume travel times between locations are known. The repairman starts and ends his day at his home, and would like to complete his work as quickly as possible. (a) What do the nodes of the graph to be constructed represent? (b). What do the edges of the graph to be constructed represent? (c). State which graph problem it is: Shortest path, Minimum spanning tree, Traveling Salesman Problem, Breadth or Depth First Search. For each of the following parts, state True or False. If true, give a short proof. If false, giver a counterexample. We are given a connected graph G with costs on edges. Assume all costs are positive and that there are no ties. A, B are nodes in the graph (1). If an edge e is part of a Minimum Spanning Tree then it cannot be part of a Maximum Spanning Tree. (2). If an edge e is part of a Shortest Path Tree rooted at A then it must also be part of a Shortest Path Tree rooted at B (3). If all edge costs are multiplied by 2 the Shortest Path Tree rooted at A remains the same tree. (4). An edge e whose cost is the largest in the graph can not be part of a Shortest Path Tree

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