This work examines a straightforward solution to a problem of satellite network resource allocation by exploring the application of an optimal algorithm to a subset of the general scheduling problem. Making some basic simplifications, such as the limitation of the mission scenarios to Low Earth Orbiting satellites, allows the effective application of the rigorous methods of the Greedy Activity-Selector algorithm. Tools such as Analytical Graphic's Satellite Tool Kit and MATLAB 5.0 are integrated to assist in the implementation of the algorithm. Several examples are presented in order to illustrate the effectiveness of the process.