# Problem 1 A company in the southwest of France needs to transport 180 tons of chemical products stored in four depots D1 to D4 to three recycling centers C1, C2, and C3. The depots D1 to D4 currently store respectively 50, 30, 35, and 65 tons of product and the recycling centers require 30, 65 and 85 tons, respectively. Two transportation modes are available: road and rail. Depot D1 only delivers to centers C1 and C2 by road at a cost of \$12,000/ton and \$11,000/ton, respectively; Depot D2 can deliver to C2, by road at a cost of \$9,000/ton and to C3 by rail or road for \$4,000/ton and \$5,000/ton, respectively; depot D3 delivers to center C1 by road at a cost 7,000/ton and to C3 by rail or road for \$9,000/ton or \$9,500/ton, respectively; depot D4 delivers to center C2 by rail or road at a cost of \$11,000/ton and \$14,000/ton, and to C3 by rail or road for \$10,000/ton and \$14,000/ton, respectively. Currently, a contract with the train transporter requires the company to transport at least 10 tons and at most 50 tons for any single delivery between the depots and centers for which the train service is available. In other words, wherever there is a rail service, between a depot and a center, the company must send at least 10 tons via that service. How should th total transportation cost? e company transport the 180 tons of chemicals to minimize the Propose a network flow formulation to solve this problem. Describe your approach using a network. Hint: try to model the two transportation options (road and rail) as a set of artificial nodes. . Use the network formulation covered in class to solve this problem. . Solve the problem using Gurobi.

Problem 1 A company in the southwest of France needs to transport 180 tons of chemical products stored in four depots D1 to D4 to three recycling centers C1, C2, and C3. The depots D1 to D4 currently store respectively 50, 30, 35, and 65 tons of product and the recycling centers require 30, 65 and 85 tons, respectively. Two transportation modes are available: road and rail. Depot D1 only delivers to centers C1 and C2 by road at a