Formulate an LP model to determine the maximum tons of sewage per hour that can be processed by this plant.

MAX:

Subject to:

Flow Through Node $1$

Flow Through Node $2$

Flow Through Node $3$

Flow Through Node $4$

Flow Through Node $5$

Flow Through Node $6$

Flow Through Node $7$

$0x_{12}7,0x_{13}8,0x_{14}8,0x_{23}8,0x_{25}9,0x_{35}7,0x_{36}6,0x_{37}8,0x_{43}7,0x_{46}10,0x_{57}10,0x_{67}12$

What is the optimal solution? $($Round your answers to three decimal places.$)$