(Solved): Consider the following network representation of a transportation problem. (i) The supplies, demand ...

Consider the following network representation of a transportation problem. (i) The supplies, demands, and transportation costs per unit are shown on the network. (a) Develop a linear programming model for this problem; be sure to define the variables in your model. Let $\begin{array}{l}{x}_{11}=\text{ amount shipped from Jefferson City to Des Moines }\\ x_{12}=\text{ amount shipped from Jefferson City to Kansas City }\\ x_{13}=\text{ amount shipped from Jefferson City to St. Louis }\\ x_{21}=\text{ amount shipped from Omaha to Des Moines }\\ x_{22}=\text{ amount shipped from Omaha to Kansas City }\\ x_{23}=\text{ amount shipped from Omaha to St. Louis }\\ \text{ Min }\\ \text{ s.t. }\\ x_{13}+\\ x_{21}+\\ x_{22}+\\ x_{23}\\ x_{11}\\ x_{12}\\ x_{13}\end{array}$ $x_{11}$ $x_{13}$ b) Solve the linear program to determine the optimal solution.