Distribution Plan to Minimize Cost. Consider the following network representation of a

transportation problem:

A network representation of a transportation problem. The diagram shows two origin nodes:

Jefferson City and Omaha with supplies $30$ and $20$; and three destination nodes: Des Moines,

Kansas City, and St$.$ Louis with demands $25,15,$ and $10.$ The origin node, Jefferson City

connects to the three destination nodes through distribution routes $($arcs$)$ that have transportation costs per unit of $14,16,$ and $7,$ respectively. The origin node, Omaha connects to

$3$

the three destination nodes through distribution routes $($arcs$)$ that have transportation costs

per unit of $8,10,$ and $5,$ respectively.

The supplies, demands, and transportation costs per unit are shown on the network. What

is the optimal $($cost minimizing$)$ distribution plan?