You have been asked to assist in the distribution design for Santa Insulators - the Brazilian's premiere source for porcelain insulators used in electrical lines. Santa Insulators operates two plants (Plant 1 in Lorena, SP and Plant 2 in Sorocaba, SP). The plants produce a range of insulator types and sizes, but you have determined that the most relevant flow unit is simply each insulator. Because the insulators are quite fragile, they are transported directly from the plants to the three DCs located in Sao Paulo, SP; Campinas, SP and Rio de Janeiro, RJ. Each DC has a different demand for insulators: Sao Paulo, SP: 6,000 insulators per week Campinas, SP: 550 insulators per week Rio de Janeiro, RJ: 3,160 insulators per week The cost of transporting an insulator from each plant to each DC ($/insulator) is shown below : $/insulator Sao Paulo, SP Campinas, SP Rio de Janeiro, RJ Plant 1 (Lorena, SP) 1.90 2.49 2.50 Plant 2 (Sorocaba, SP) 1.01 0.86 5.27 The plants have their differences, but they have the same capacity of 5,000 insulators/week. The Chief Financial Officer for Santa Insulators, Paulo Silva, believes that the models are not including the cost of running a production line at a plant. He tells you that to manage a production line of one product type costs $5,000 per week. So, if a plant is producing both Type A and Type B insulators, they incur a $10,000 fixed cost. How should we adjust the variables and constraints in the model to implement the changes requested by the CFO?

Add two binary variables to represent opening each of the two plants.

Add four binary variables to represent opening each of the two production line types at each of the two plants.

Add two binary variables to represent opening each of the two production lines.

Add four new constraints to allow outbound shipments of either product type from either plant only if the corresponding production line is open.

Add two new constraints to allow outbound shipments from a plant only if it is open.