(1) The CoolAire Company manufactures air conditioners that are sold to three different Retail customers across the United States. The company is evaluating its manufacturing and logistics strategy to ensure that it is operating in the most efficient manner possible. The company can produce air conditioners at two plants across the country and stock these units in any of three warehouses. The cost of manufacturing and shipping a unit between each plant and warehouse is summarized in the following table along with the monthly capacity and fixed cost of operating each plant. (20 points) Plant 1 Plant 2 Warehouse 1 700$ 800$ Warehouse 2 Warehouse 3 1,000$ 900$ 500$ 600$ Fixed cost capacity 55,00$ 300 40,00$ 200 Similarly, the per-unit cost of shipping units from each warehouse to each customer is given below, along with the monthly fixed cost of operating each warehouse. Warehouse 1 Warehouse 2 Warehouse 3 Customer 1 70$ 80$ 80$ Customer 2 1,00$ 50$ 50$ Customer 3 90$ 60$ 60$ Fixed cost 55,00$ 40,00$ 40,00$ The monthly demand from each customer is summarized below. Customer 1 100 Customer 2 50 Customer 3 30 Demand Create a mathematical model for this problem to determine which plants and warehouses should CoolAire operate and what is the optimal shipping plan? (1) The CoolAire Company manufactures air conditioners that are sold to three different Retail customers across the United States. The company is evaluating its manufacturing and logistics strategy to ensure that it is operating in the most efficient manner possible. The company can produce air conditioners at two plants across the country and stock these units in any of three warehouses. The cost of manufacturing and shipping a unit between each plant and warehouse is summarized in the following table along with the monthly capacity and fixed cost of operating each plant. (20 points) Plant 1 Plant 2 Warehouse 1 700$ 800$ Warehouse 2 Warehouse 3 1,000$ 900$ 500$ 600$ Fixed cost capacity 55,00$ 300 40,00$ 200 Similarly, the per-unit cost of shipping units from each warehouse to each customer is given below, along with the monthly fixed cost of operating each warehouse. Warehouse 1 Warehouse 2 Warehouse 3 Customer 1 70$ 80$ 80$ Customer 2 1,00$ 50$ 50$ Customer 3 90$ 60$ 60$ Fixed cost 55,00$ 40,00$ 40,00$ The monthly demand from each customer is summarized below. Customer 1 100 Customer 2 50 Customer 3 30 Demand Create a mathematical model for this problem to determine which plants and warehouses should CoolAire operate and what is the optimal shipping plan