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:

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) Describe how this problem fits the network description of the minimum spanning tree problem.
(b) Use the algorithm described in Sec. 10.4 to solve the problem.

Distance between Pairs of Offices Main B. B B. B.4B.5 70 115 270 160 50 140 120 220 80 310 190 Main office Branch 1 Branch 2 Branch 3 Branch 4 Branch 5 100 110 215 -175 80 310 190 70 115 100 110 140 270 215 20 175 160 50 220