3. [Inspired from Powell and Baker, Chapter 10] This problem is a typical logistics problem that appears in many supply chains. Consider a manufacturing company who owns two factories. The manufactured products are shipped to three distribution centers (DC). The products are then shipped to three warehouses. The shipping costs for a unit of product from factories to distribution centers is provided below: Dist Center 1 Rist Center 2 Dist Center 3 Factories/ Distribution Centers Factory 1 Factory 2 $1.25 $1.34 $1.35 $1.26 $1.30 $1.55 The shipping costs for a unit of product from distribution centers to warehouses is provided below: Warehouse 1 Warehouse 2 Warehouse 3 Dist Centers/ Warehouses Dist Center 1 Dist Center 2 Dist Center 3 $0.60 $0.57 $0.67 $0.50 $0.30 $0.58 $0.43 $0.38 $0.35 Each factory has a capacity. Factory 1 can produce 3000 units while factory 2 can produce 2700 units. The demand in each warehouse is as follows: Warehouse 1 (1300 units), warehouse 2 (1500 units), and warehouse 3 (1400 units). How many units should be shipped from each factory to each distribution center and from each distribution center to each warehouse to minimize the shipping costs in this network? Hints: 1. Notice that this is a two-stage shipment problem in which the first stage of shipments happens from factories to distribution centers, and the second stage of shipments happens from the distribution centers to the warehouses. 2. Denote the decision variables in the first stage by x and the decision variables in the second stage by y. For example, X11 would correspond quantity shipped from factory 1 to distribution center 1, and y11 would correspond to quantity shipped from distribution center 1 to warehouse 1. 3. Notice that the distribution centers serve as transshipment points. Therefore, what goes into a distribution center should come out. Make sure to write the constraints that would represent this situation. 3. [Inspired from Powell and Baker, Chapter 10] This problem is a typical logistics problem that appears in many supply chains. Consider a manufacturing company who owns two factories. The manufactured products are shipped to three distribution centers (DC). The products are then shipped to three warehouses. The shipping costs for a unit of product from factories to distribution centers is provided below: Dist Center 1 Rist Center 2 Dist Center 3 Factories/ Distribution Centers Factory 1 Factory 2 $1.25 $1.34 $1.35 $1.26 $1.30 $1.55 The shipping costs for a unit of product from distribution centers to warehouses is provided below: Warehouse 1 Warehouse 2 Warehouse 3 Dist Centers/ Warehouses Dist Center 1 Dist Center 2 Dist Center 3 $0.60 $0.57 $0.67 $0.50 $0.30 $0.58 $0.43 $0.38 $0.35 Each factory has a capacity. Factory 1 can produce 3000 units while factory 2 can produce 2700 units. The demand in each warehouse is as follows: Warehouse 1 (1300 units), warehouse 2 (1500 units), and warehouse 3 (1400 units). How many units should be shipped from each factory to each distribution center and from each distribution center to each warehouse to minimize the shipping costs in this network? Hints: 1. Notice that this is a two-stage shipment problem in which the first stage of shipments happens from factories to distribution centers, and the second stage of shipments happens from the distribution centers to the warehouses. 2. Denote the decision variables in the first stage by x and the decision variables in the second stage by y. For example, X11 would correspond quantity shipped from factory 1 to distribution center 1, and y11 would correspond to quantity shipped from distribution center 1 to warehouse 1. 3. Notice that the distribution centers serve as transshipment points. Therefore, what goes into a distribution center should come out. Make sure to write the constraints that would represent this situation