4. (30 points) A simple transportation network is shown in the figure below. Both factories 1 and 2 are producing a certain product to supply for warehouses 1, 2 and 3. The arrows represent the transporting path between factories and warehouses and the numbers on the arrows represent the cost of shipping each unit product on that path. For example, from factory 1 to warehouse 2, the cost of shipping is 6 dollars per unit. The supply capacity of each factory is 30 units, and demand requirements of warehouse 1, 2 and 3 is 10, 30 and 20 units respectively, as shown in the figure. For example, factory 1 is capable of producing 30 units and warehouse 1 needs at least 10 units. Please construct a LP model to minimize the shipping cost based on the information above. Supply 30 warehouse 1 Factory 1 ABBBBBBB Demand LABERABES warehouse 2 Demand 30 Supply 30 30 ML 27 Demand Factory 2 LABBBBBB warehouse 3 20 Note: (1) No need to solved it. Only objective function and constraints are needed here. (2) Please specify the decision variable first, then use the decision variable to construct the objective function and constraints