Consider the following network representation of a transportation problem.

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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: $35$

Omaha: $40$

Des Moines: $20$

Kansas City: $10$

St$.$ Louis: $45$

Jefferson City$$Des Moines: $14$

Jefferson City$$Kansas City: $9$

Jefferson City$$St$.$ Louis: $8$

Omaha$$Des Moines: $8$

Omaha$$Kansas City: $10$

Omaha$$St$.$ Louis: $23$

The supplies, demands, and transportation costs per unit are shown on the network. What is the optimal $($cost minimizing$)$ distribution plan?

Amount Cost

Jefferson City$$Des Moines

Jefferson City$$Kansas City

Jefferson City$$St$.$ Louis

Omaha$$Des Moines

Omaha$$Kansas City

Omaha$$St$.$ Louis

Total