This paper addresses the optimal allotment of ground station support time to low orbit (LEO) spacecraft with clashing visibilities. Orbiting once every 100 or so minutes at a 800 km height, LEOs now form a critical infrastructure for natural resource management, rescue, crop yield estimation, flood control, communication, and space research and travel support worldwide. This problem is a generalization of the classical product mix problem in which “production quantities” (representing support times) must be determined so as to maximize total profits to the enterprise while subject to a multitude of constraints. The problem is NP-complete. The present methodology exploits the structure of the profit function and constraints and invokes meta-heuristic methods to determine the optimum allocation. The paper concludes with the solution of a practical satellite support optimization problem routinely faced by mission managers. An important spin-off of this work is that it can enable the decision maker to also determine optimal ground station locations and support capability deployment in widely diverse scenarios.