Distribution Network Planning. The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit $($in $$)$ from each plant to each warehouse are as follows:Customer demand and shipping costs per unit $($in $$)$ from each warehouse to each cus$-$tomer are as follows. LO $3$a$.$Develop a network representation of this problem.b$.$Formulate a linear programming model of the problem.c$.$Solve the linear program to determine the optimal shipping plan$\mathrm{.}12.$Distribution Network Planning $($revisited$).$ Refer to Problem $11.$ Suppose that ship$-$ments between the two warehouses are permitted at $$2$ per unit and that direct ship$-$ments can be made from Plant $3$ to Customer $4$ at a cost of $$7$ per unit. LO $3$a$.$Develop a network representation of this problem.b$.$Formulate a linear programming model of this problem.c$.$Solve the linear program to determine the optimal shipping plan