use lingo software and provide the min function along with the constraints. $4.$ 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 $($ares$)$ 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 costh per unit are shown on the network. What is the optimal $($cost minimixing$)$ distribution plan?