1. The Premiere Bank will soon 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: Main Office Branch 1 Branch 2 Branch 3 Branch 4 Branch 5 Distance between Pairs of Offices Main B.1 B.2 B.3 B.4 B.5 190 160 115 270 60 190 50 110 215 100 160 50 80 310 220 115 110 80 175 140 270 215 310 175 120 60 100 220 140 120 1 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) (points: 3) Describe how this problem fits the network description of the minimum spanning tree problem: Identify the vertices, edges and the edge weights. (b) (points: 5) Use Prims algorithm to solve the problem. Use the tabular form