Question $2)$ Formulate a maximum flow problem LP for. $-$ network described below $($assume that flow is from left to right $($all lines are arcs$).$ Draw the network diagram 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$1,2,$ and R$2$ can be estimated to be 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.

R$1$

R$2$

R$3$

A

B

C

D

E

F

T

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.

To

From

R$1$

R$2$

R$3$

To

To

A B C From

$130115$

$7090110$

$140120$

DEF From

$11085-$

$1309585$

$130160$

D

W L

T

$220$

$330$

$240$

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