A graph with $10$ nodes and $18$ directed arcs is shown.

Node $1$ is connected to node $2$ by arc of value $500,$ to node $5$ by arc of value $300,$ and to node $6$ by arc of value $600.$

Node $2$ is connected to node $3$ by arc of value $300$ and to node $4$ by arc of value $400.$

Node $3$ is connected to node $4$ by arc of value $150.$

Node $4$ is connected to node $8$ by arc of value $400$ and to node $10$ by arc of value $600.$

Node $5$ is connected to node $7$ by arc of value $400.$

Node $6$ is connected to node $7$ by arc of value $300$ and to node $9$ by arc of value $500.$

Node $7$ is connected to node $6$ by arc of value $200$ and to node $9$ by arc of value $350.$

Node $8$ is connected to node $4$ by arc of value $200,$ to node $9$ by arc of value $300,$ and to node $10$ by arc of value $450.$

Node $9$ is connected to node $8$ by arc of value $300$ and to node $10$ by arc of value $500.$

Node $10$ has no directed arcs directed to other nodes.

Formulate an LP to find the maximal flow in cars per hour from node $1$ to node $10.($Let xij 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

Node $7$ Flows

Node $8$ Flows

Node $9$ Flows

Node F Flows

Max Flow on Arcs

all xij $>=0$ for all i and j