HOMEWORK The Minimum Spanning Tree and The Shortest Path Problem 1. The Premiere Bank soon will be hooking up computer terminals at each of its branch offices to the computer at its main office using special phone lines with telecommunications devices. The phone line from a branch office need not be connected directly to the main office. It can be connected indirectly by being connected to another branch office that is connected (directly or indirectly) to the main office. The only requirement is that every branch office be connected by some route to the main office. The charge for the special phone lines is $100 times the number of miles involved, where the distance (in miles) between every pair of offices is as follows: Distance between Pairs of Offices Main B.1 B.2 B.3 B.4 B.5 190 70 100 115 110 140 Main office Branch 1 Branch 2 Branch 3 Branch 4 Branch 5 190 70 115 270 270 215 120 175 100 110 215 50 160 50 220 80 310 140 120 220 175 80 160 310 Management wishes to determine which pairs of offices should be directly connected by special phone lines in order to connect every branch office (directly or indirectly) to the main office at a minimum total cost. (a) Solve the minimum spanning tree problem. (b) Determine the total length of the links. (c) Determine the total cost in order to connect every branch office to the main office