Problem 1: A small milk processing company is committed to delivering milk to five supermarkets in the region. The company has four tanker trucks with the capacities and cost values given in the table below. Truck 1 Truck 2 Truck 3 Truck 4 Capacity (Barrel) 400 500 600 1100 Cost (100) 4.5 5.0 5.5 6.0 Each supermarket's milk demand can be delivered by only one truck. However, a truck can serve more than one supermarket. The milk demand of the supermarkets is 100, 200, 300, 500 and 800 tons, respectively. Formulate the optimum milk distribution problem at minimum cost. The following represents an electrical power distribution network connecting power generating points G1 to G4 with power consuming points C through C4. The arcs are undirected, i.e., power may flow in either direction. The generating capacities and unit costs are given by the following table. Generator G2 G3 60 80 13.5 21 G] 100 15 Capacity (thousands of KWH) Unit Cost ($ per thousands of KWH) G4 150 23.5 The power consumption for points C through C is 35K, 50K, 60K, and 40K respectively. There is no capacity limitation on the transmission lines and the unit cost of transmission is $11 per 1000 KWH on all lines. Note that supply exceeds demand. G2 GI G4 03 Formulate the problem of finding the optimal power allocation as a minimum cost network flow problem (Hint: you may have to introduce additional arcs and/or nodes)