The Synthetic Theater Operations Research Model (STORM) simulates theater-level conflict and requires inputs about utilization of surveillance satellites to search large geographical areas. We develop a mixed-integer linear optimization model that prescribes plans for how satellites and their sensors should be directed to best search an area of operations. It also specifies the resolution levels employed by the sensors to ensure a suitable fidelity of the resulting images. We solve large-scale instances of the model involving up to 22 million variables and 11 million constraints in scenarios derived from STORM. On average, the model yields 55% improvement in search coverage relative to an existing heuristic algorithm in STORM.