Consider the network below.

A graph with $7$ nodes and $10$ arcs is shown.

Node $1$ is connected to node $2$ by arc of value $9$ and to node $3$ by arc of value $12.$

Node $2$ is connected to node $4$ by arc of value $3$ and to node $5$ by arc of value $7.$

Node $3$ is connected to node $5$ by arc of value $8$ and to node $6$ by arc of value $8.$

Node $4$ is connected to node $2$ by arc of value $3,$ to node $5$ by arc of value $3,$ and to node $7$ by arc of value $7.$

Node $5$ is connected to node $2$ by arc of value $7,$ to node $3$ by arc of value $8,$ to node $4$ by arc of value $3,$ and to node $7$ by arc of value $5.$

Node $6$ is connected to node $3$ by arc of value $8$ and to node $7$ by arc of value $3.$

Formulate the LP for finding the shortest$-$route path from node $1$ to node $7.$

Min

s$.$t$.$

Node $1$ Flows

Node $2$ Flows

Node $3$ Flows

Node $4$ Flows

Node $5$ Flows

Node $6$ Flows

Node $7$ Flows