PROBLEM 2 (20 points) Interstate Warehousing offers cold storage services for meat and sea product companies. Its facilities are used to receive and temporarily store frozen meats and fish from manufacturers, and ship to demand areas as demand arises. Bubba-Gump Shrimp Co. operates out of two cities: Galveston, TX, and Sarasota, FL. Some of its biggest customers are located in Cincinnati, OH , and Pittsburg, PA. To service BubbaGump Shrimp Co., Interstate Warehousing plans to build new cold storage facilities. Interstate Warehousing selected two potential locations for new cold storage facilities: Roanoke, VA, and Knoxville, TN. Land is more expensive in Knoxville, so if Interstate Warehousing chooses to build a facility in Knoxville, it will cost $405 , 000 per year to operate, while facility in Roanoke will cost $280 , 000 per year. Table 1 below contains costs of shipping of 1 ton of shrimp from Galveston and Sarasota to cold storage facilities in Knoxville and Roanoke, as well as supply (in tons), available in Galveston and Sarasota: Table 1 Table 2 below contains costs of transportation of 1 ton of shrimps from cold storage facilities in Knoxville and Roanoke to markets in Cincinnati and Pittsburg, as well as demands in Cincinnati and Pittsburg: Table 2 Interstate Warehousing must decide where to build warehouses (Knoxville, or Roanoke, or both) and how to ship product between Galveston and Sarasota and warehouses, and between warehouses and Cincinnati and Pittsburg to minimize total cost of product transportation and warehouse operations. On the schematic picture below defined are decision variables. Xij is the number of tons of shrimp shipped from source i to destination j . For example, XGK is number of tons shipped form Galveston ( G ) to Knoxville ( K ) . Y l ? and Y 2 ? are binary variables. If Y l ? = 1 then Knoxville warehouse should be build, if Y 2 ? = 1 then Roanoke warehouse should be build. a) (5 points) Write down the mathematical expression for the objective function using variables defined above. Make sure to specify if this is a min or max problem. NOTE: use decision variables defined on picture above. b) (15 points) Write down expressions ? for all applicable constraints, using the decision variables, defined above. For each constraint briefly indicate what does it represent. Do NOT solve this problem with Excel. HINT: you should have supply, demand, and transshipment constraints, as well as "big M" constraints for possible cold storage warehouses. NOTE: use decision variables defined on picture above