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$)$ 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.