Discussion on mathematical model of rational location selection and scientific layout of national fitness route

National fitness route is an important site for people´s fitness activities in China and with its increasing popularity, how to select rational sites and conduct scientific layout, it grows quite urgent. In order to give full play to the national fitness route, the paper, based on the actual number of fund collected, intends to coordinate the site selection for national fitness and optimize its layout scientifically to meet the needs of the people maximally. This paper modeled the problem in that there are n residential areas (referred to as Collection), numbered from p ₁, p ₂, ..., p_n with their location coordinates known as p₁ (x₁, x₂), p₂ (x₂, y₂), ..., p_n (x_n, y_n respectively, and w_i inhabitants. To establish m national fitness routes q_i (u_j, u_j), we assume residents in each district can have access to only one fitness route to do fitness exercise. The question is that how to plan and lay out the m fitness routes enables the shortest total distance C for all residents´ reach to their fitness route. In this paper, the Location Model in Operational Research is employed to make an analytical study on this issue to establish the location model and mean while gives mathematical solutions to the model in detail.