1. Shipping Schedule A manufacturer has three plants and four warehouses. Each plant has a potential capacity, expressed in cartons of product, and each warehouse has a demand requirement for the week that must be met. There are 12 possible shipment routes, and for every plant-warehouse combination, the unit shipping cost is known. The following table provides the given information. (From) plant Atlanta Boston Chicago Denver Capacity Minneapolis $0.60 $0.56 $0.22 $0.40 10,000 Pittsburgh 0.36 0.30 0.28 0.58 15,000 Tucson 0.65 0.68 0.55 0.42 15,000 Requirement 8000 10,000 12,000 9000 The product is subject to evaporation in the tanker trucks used for distribution purposes. The average amount of evaporation depends the distance traveled and the average temperature. The following table shows the corresponding yield loss as it has been observed to occur on each of its shipping routes. (From) plant Atlanta Boston Chicago Denver Minneapolis 0.24 0.19 0.07 0.11 Pittsburgh 0.10 0.05 0.04 0.15 Tucson 0.26 0.41 0.32 0.27 (a) [4pts] What is the minimal shipping cost and the associated optimal shipping schedule? (b) [3pts] A new type of tanker trucks can completely eliminate the yield loss. If the manufacturer can replace its fleet with the new trucks, how much can it save on shipping cost (with possibly new schedule)? How should it change the optimal shipping schedule