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This study addresses the optimal allotment of ground station support time to low Earth orbit (LEO) spacecraft with clashing radio visibilities. LEOs now form a critical global infrastructure for natural resource management, rescue, crop yield estimation, flood control, communication, and space research and travel support. In the multi-spacecraft scenario, ground support becomes complex because of spacecraft-specific constraints, station configuration, spacecraft priorities and priorities of payload and special operations. A generalization of the classical product mix problem, spacecraft support is NP-complete and more complex than the former because of arbitrarily defined profitability profile. Genetic algorithms (GA) are used to near optimally resolve visibility clashes. It concludes with the illustration of real life spacecraft support optimization problems routinely faced by mission managers. A 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 diverse planning scenarios.