TechValley Inc. soon will be hooking up computer terminals at each of its branch offices in the UK to the computer at its main office using special fibre optic lines with telecommunications devices. The fibre optic 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 cost for the special optical fibre lines is $1,000$ 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 Office Branch $1$ Branch $2$ Branch $3$ Branch $4$ Branch $5$

Main Office $---19070115270160$

Branch $1190---10011021550$

Branch $270100---140120220$

Branch $3115110140---17580$

Branch $4270215120175---310$

Branch $51605022080310---$

Management wishes to determine which pairs of offices should be directly connected by special optical fibre lines in order to connect every branch office $($directly or indirectly$)$ to the main office at a minimum total cost.

Managerial report:

Write a report including a critical appraisal that includes the minimal spanning tree analysis of the network and associated cost of TechValley Inc. to connect its offices through the optical fibre cable.