accommodated. $($Let $x_{ij}$ represent the tons of sewage per hour that flows from node $i$ to node $j.)$

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 $7$

X

X

X

X

X

X

X

X

X

X

X

X

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

$($X$12,$ X$13,$ X$14,$ X$23,$ X$25,$ X$35,$ X$36,$ X$37,$ X$43,$ X$46,$ X$57,$ X$67)=$