) The Company SUPER3PO produces and distributes the orders by its own network. The products are prepared in 2 plants of the company. Then these products are sent to one of the 2 warehouses. Finally, the 5 retailers rec the shipments from either one or both warehouses. Since each plant has slightly different technologies, each a different capacity and unit cost of production. Similarly, each warehouse has a different capacity and unit cos handling per product. The cost of transporting, producing and handling per product, production and hand capacities of each plant and warehouse and the demand of each retailer are given in tables 1 -3. (1) (2) (3) (4) (5) (6) (7) (8) /product Warehouse 1 Plant Retailer 2 1 2 3 4 5 1 10 17 6 5 7 14 15 2 20 8 9 8 11 7 4 Table 1: The transportation cost per product from the plants to the warehouses (columns 2-3) and from the warehouses to the retailers (columns 4-8). (1) Plant (2) 1 (3) 2 Capacity (product) 460 Cost (/product) 15 420 12 (4) (5) (6) Warehouse Capacity (product) Cost (/product) 1 2 550 450 1 2 Table 2: The production capacity per day and cost of each plant (left) and, the handling capacity per day and cost of each warehouse (right). Retailer Demand 1 2 3 100 150 180 Table 3: The daily demand of each retailer. 4 5 200 170 Formulate a mathematical model that will help the company to satisfy the retailers demand with minimum cost. Please describe the indices, parameters, variables, objective function and constraints. Please also briefly describe your constraints.