Question $2)$ Formulate a maximum flow problem LP for the network described below $($assume that flow is from left to right $($all lines are ares$).$ Draw the network dliagram with arc capacities on each arc. You may want to introduce hypothetical source node at the beginning. The arc capacities from source node to $R_1,R_2,$ and $R_2$ can be estimated to he equivalent to the total arc capacities going out of $R_1,$ R$2,$ R$3,$ respectively.$)$

$9\mathrm{.}5-3.$ The next diagram depicts a system of aqueducts that originate at three rivers $($nodes R$1,$ R$2,$ and R$3)$ and terminate at a major city $($node T$),$ where the other nodes are junction points in the system.

Using units of thousands of acre feet, the tables below the diagram show the maximum amount of water that can be pumped through each aqueduct per day.

$\backslash$table$[[$From$,A,$B$,$C$,$From,D$,$E$,$F$,$From,$],[$R$1,130,115,-,$A$,110,85,-,$D$,220],[$R$2,70,90,110,$B$,130,95,85,$E$,330],[$R$3,-,140,120,$C$,1-,130,160,$F$,240]]$

The city water manager wants to determine a flow plan that will maximize the flow of water to the city.