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.

Task $1[20$ points$]$: Using LINDO, solve your model and show the optimal solution on the network.

Task points$]$: Using GAMS, solve your model.