Consider the network below. Nodes in the network represent the six cities of a country. The numbers

on the lines connecting the nodes show the distance between cities in kilometers.

The following questions in parts $($a$)$ and $($b$)$ are independent of each other.

$($a$)$ There is a hydropower plant located at node $1.$ We want to establish a line between the cities to

provide electricity to all of them. Write a mathematical model that will connect all cities with

minimum total length. For that purpose, define all decision variables with the appropriate

notation. Write the objective function and all constraints. Verbally explain them. Do the

following tasks.