Rand$-$mobile has decided that the different arcs $($linkages$)$ in Question $2$ from the first area $($node $1)$ to the sixth area $($node $6)$ are unidirectional $($single

direction$).$ For example $(2,3)$ Indicates a connection between areas$($nodes$)2$ and $3.$ In addition, the direction of the connection is only from $2$ to $3.$ All the

connections point in the direction of the higher nodes.

e$.$g$.(2,3)$

Rand$-$Mobile needs to explore the possibility of using a mathematical programming tool $($AMPL$)$ to determine the following:

$($a$)$ Maximum amount of messages that could be sent between the first and sixth geographical area.$[5]$

$($b$)$ The most inefficient message route between the first and sixth geographical areas.$[5]$

Hint: AMPL solutions should be attached as clear and legible screenshots in PDF format to show the AMPL editor and command console.