A graph with 6 nodes and 13 directed arcs is shown.

Node 1 is connected to node 2 by arc of value 17, to node 3 by arc of value 19, and to node 5 by arc of value 9.

Node 2 is connected to node 3 by arc of value 8 and to node 4 by arc of value 14.

Node 3 is connected to node 2 by arc of value 5, to node 4 by arc of value 9, to node 5 by arc of value 7, and to node 6 by arc of value 24.

Node 4 is connected to node 3 by arc of value 9 and to node 6 by arc of value 13.

Node 5 is connected to node 3 by arc of value 7 and to node 6 by arc of value 11.

Node 6 has no directed arcs directed to other nodes.

The network below shows the flows possible between pairs of six locations.

A graph with 6 nodes and 13 directed arcs is shown.

Node 1 is connected to node 2 by arc of value 17, to node 3 by arc of value 19, and to node 5 by arc of value 9.

Node 2 is connected to node 3 by arc of value 8 and to node 4 by arc of value 14.

Node 3 is connected to node 2 by arc of value 5, to node 4 by arc of value 9, to node 5 by arc of value 7, and to node 6 by arc of value 24.

Node 4 is connected to node 3 by arc of value 9 and to node 6 by arc of value 13.

Node 5 is connected to node 3 by arc of value 7 and to node 6 by arc of value 11.

Node 6 has no directed arcs directed to other nodes.

Formulate an LP to find the maximal flow possible from node 1 to node 6. (Let x_ij represent the flow from node i to node j. Enter your maximum flows as a comma-separated list of inequalities.)

Max

s. t.

Node 1 Flows

Node 2 Flows

Node 3 Flows

Node 4 Flows

Node 5 Flows

Node 6 Flows

Max Flow on Arcs