$1.$ Consider the following transshipment problem. The distribution system consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit $($in $$)$ from each plant to each warehouse are as follows: Warehouse Plant $12$ Capacity $147450285600356380$ Customer demand and shipping costs per unit $($in $$)$ from each warehouse to each customer are as follows: Warehouse $12341648423677$ Demand $300300300400$ a$)$ Develop a network representation of this problem. b$)$ Develop a spreadsheet model and solve to determine the optimal shipping plan. $2.$ Consider Problem $1.$ Suppose that shipments between the two warehouses are permitted at $$2$ per unit and that direct shipments can be made from Plant $3$ to Customer $4$ at a cost of $$7$ per unit. a$)$ Develop a network representation of this problem. b$)$ Develop a spreadsheet model and solve to determine the optimal shipping plan.