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:

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 Prim$$s algorithm to solve the problem. Use the tabular form