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.

Using the Miller$-$Tucker$-$Zemlin formulation, write a mathematical model that will minimize the

total distance traveled by a vehicle that leaves city $1,$ visits all cities only once, and then returns

to city $1.$ For that purpose, define all decision variables with the appropriate notation. Write the

objective function and all constraints. Verbally explain them.

Write the code in LINDO and Gams that shows the optimal solution