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Part II: Problem 1 (20) A supply chain for ABC company consists of three plants, two warehouses, and three retail stores. Plant capacities and shipping costs per unit from each plant to each warehouse are listed in the following table, Table 1: Shipping cost (S/unit) Plant to Warehouse and Plant capacity Warehouse Plant S4 S7 2 S8 $5 Capacity (units) 450 600 S5 S6 380 Shipping costs from each warehouse to each retail store and store demand are listed in the following table Table 2: Shipping cost (S/unit) Plant to Warehouse and Retail Store Demand Retail Stores Warehouse 1 1 S6 $ 4 98 S3 S6 S7 Demand 1300 1300 1300 2 The operation manager wishes to determine the minimum-cost shipping plan. Find: a) Develop a network diagram of the above problem (5) Part II: Problem 1 (cont'd) b) Formulate the above problem as a linear program. Clearly define the decision variables, objective function, and constraints. General Expressions are not acceptable b.1) Decision Variables: (5) b.2) Objective Function: (5) 6.3) Constraints