Consider the following network representation of a transportation problem: 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. If constant is $"1",$ it must be entered in the box.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. If constant is $"1",$ it must be entered in the box. Let $\backslash ($ x$\_\{$i j$\}=\backslash )$ amount shipped from supply node $\backslash ($ i $\backslash )$ to demand node $\backslash ($ j $\backslash ).$ b$.$ Solve the linear program to determine the optimal solution. Enter $"0"$ if your answer is zero.