e $8777635348141678105$

A network diagram between five locations is shown. The left$-$hand side of the graph is labeled "Supplies" and lists Jefferson City and Omaha. The right$-$hand side of the graph is labeled "Demands" and lists Des Moines, Kansas City, and St$.$ Louis. Lines are shown between various locations. The following list contains the numbers placed on the graph.

Jefferson City: $87$

Omaha: $77$

Des Moines: $63$

Kansas City: $53$

St$.$ Louis: $48$

Jefferson City$$Des Moines: $14$

Jefferson City$$Kansas City: $16$

Jefferson City$$St$.$ Louis: $7$

Omaha$$Des Moines: $8$

Omaha$$Kansas City: $10$

Omaha$$St$.$ Louis: $5$

The supplies, demands, and transportation costs per unit are shown on the network. The optimal $($cost minimizing$)$ distribution plan is given below. $($Assume x$11=$ amount shipped from Jefferson City to Des Moines, x$12=$ amount shipped from Jefferson City to Kansas City, x$13=$ amount shipped from Jefferson City to St$.$ Louis, x$21=$ amount shipped from Omaha to Des Moines, x$22=$ amount shipped from Omaha to Kansas City, and x$23=$ amount shipped from Omaha to St$.$ Louis.$)$

Des Moines Kansas City St$.$ Louis Supply

Jefferson City $3904887$

Omaha $2453077$

Demand $635348$

Use the procedure described in Section $12\mathrm{.}7$ to try to find an alternative optimal solution. $($Round your answers to the nearest integer.$)$

$($x$11,$ x$12,$ x$13,$ x$21,$ x$22,$ x$23)=$