Warehouse Location The FMC Corporation* The FMC Corporation is a large diversified producer of machinery, chemicals, films, and fibers such as nylon. The company has annual sales which place it in the top hundred corporations in the nation. The study presented in this case was done for FMC's Link-Belt Products Division, manufacturers of a broad line of industrial equipment. The study was done by FMC's own consultants, people who are available to work with any of the company's divisions A few years before the beginning of this study, Link-Belt management began to feel that perhaps it should reduce the number of warehouses. This feeling was based on several factors, including the decrease in transportation time necessary to reach customers, the lower cost of communication services, higher labor costs, and improvements in techniques of automating warehouses The company had warehouses in Philadelphia; Atlanta, Columbus, Ohio, Chicago, Kansas City; Dallas, Reno, Seattle, Houston; and Portland, Oregon. The question presented by the Link-Belt management to the consultants: Should any of the current warehouses be closed, and, in general, what possible configuration of warehouse sites would provide the lowest possible cost while still providing good service to customers? Dollar amounts reflecting total warehouse sales, tonnages handled, and total operating costs are considered confidential by FMC. However, in the most recent year for which an analysis of figures could be made, the percentage breakdown for Link-Belt's warehouse operating costs were as follows 19% for freight, 42% for inventory investment, and 39% for operating expenses To begin the analysis, 17 additional cities were selected as potential warehouse sites. Since construction and land costs vary from city to city, it was necessary to develop for each city an equation which represented the local costs of construction. In developing this equation, we shall use the following variable A warehouse floor area (in thousands of square feet) Cccost of labor and materials to build a warehouse (in thousands of dollars) L = amount of land needed for warehouse (in acres) C1 cost of land (in thousands of dollars) Iinventory in a warehouse at a given time (in pounds) T-total quantity of merchandise going through a warehouse in a year (in thousands of pounds) For example, if A represents the warehouse area in thousands of square feet, and Cc represents the cost of labor and materials in thousands of dollars, thern