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

$x_{11}=$ 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

$x_{23}=$ amount shipped from Omaha to St$.$ Louis