Facility location is a branch of Operations Research and computational geometry concerning itself with mathematical modeling and solution of problems concerning optimal placement of facilities in order to minimize transportation costs, avoid placing hazardous facilities near housing, etc. One of the greatest problems facing both the public and the private sector enterprises is how to locate facilities. People site their facilities anywhere and anyhow without first considering how close that facility will be to people in the community and whether the facility is desirable, semi desirable or undesirable by the community. This work attempts to use p-median model to find a suitable site to locate a library facility at Nkoranza community. Two different methods were used to locate the facilities; the myopic algorithm and Lagrangian algorithm. Results of both algorithm suggest that we locate the facility at Kassadjan. The optimal objective function value was 92674 kilometers. This gave an average demand-weighted distance of 2.06 km.