$($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

$Min{x}_{11}+x_{12}+x_{13}+8,x_{21}+,x_{22}+25$

$s.t.x_{11}+x_{12}+x_{13}$

$x_{11}$

$x_{12}$

$x_{21}$

$x_{22}$

$+,x_{21}$

$x_{13}$

$x_{11},x_{12},x_{13},x_{21},x_{22},x_{23}0$

$($b$)$ Solve the linear program to determine the optimal solution.