solve with lingo and represent the solution in a network diagram

Sunco Oil wants to ship the maximum possible amount of oil (per hour) via pipeline from node so to node si in Figure 6. On its way from node so to node si, oil must pass through some or all of stations 1, 2, and 3. The various arcs represent pipelines of different diameters. The maximum number of barrels of oil (millions of barrels per hour) that can be pumped through each arc is shown in the Table . Each number is called an arc capacity. Formulate an LP that can be used to determine the maximum number of barrels of oil per hour that can be sent from so to si.

Arc Capacities for Sunco Dill \begin{tabular}{lc} \hline Arc & Capacity \\ \hline( so, 1) & 2 \\ ( so, 2) & 3 \\ (1,2) & 3 \\ (1,3) & 4 \\ (3,si) & 1 \\ (2,si) & 2 \\ \hline \end{tabular} Arc Capacities for Sunco Dill \begin{tabular}{lc} \hline Arc & Capacity \\ \hline( so, 1) & 2 \\ ( so, 2) & 3 \\ (1,2) & 3 \\ (1,3) & 4 \\ (3,si) & 1 \\ (2,si) & 2 \\ \hline \end{tabular}