During the past two decades, mathematical programing techniques have been widely utilized in the private sector for optimization studies in locating industrial plants, scheduling commodity flows, determining product mix, etc. However, their use in the public sector has been less extensive, partly because of the absence of a clear-cut profit motive and partly because of the difficulty involved in expressing public planning problems strictly in terms of economic variables. This report describes a case study carried out in Chicago, in which an integer programing technique was used to investigate a basic problem in planning allocation of attendance areas. The study demonstrates that programing techniques can also be useful for planning public facilities such as schools. While the particular results reported are specific to the case study, the mathematical model described and tested is generic and can readily be adapted to other areas. (Author)