use industrial engineering operations reseach $,$The Rand$-$mobile phone company services six geographical areas. The satellite distances $($in miles$)$ among the six areas are given in Table $1.$ Note that the

arcs linking the areas $($nodes$)$ are undirectional $($no direction$).$

Nodes $=1,2,3,4,$ and $5$

Arcs $=\{(1,2),(1,3),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)\}$

Table $1$: Distances of the undirectional arcs

$($a$)$ Draw the network defined by the Nodes and Arcs. $[2]$

$($b$)$ Determine for Rand$-$mobile the most efficient message routes that should be established between each two areas $($nodes$)$ in the network using the most

appropriate algorithm discussed in class.$[8]$