The correct answer is B) U.S. Coast Guard. The AMVER (Automated Mutual-Assistance Vessel Rescue) system is administered by the United States Coast Guard. AMVER is a worldwide voluntary ship reporting system used by search and rescue authorities to aid vessels in distress. As the primary maritime law enforcement agency in the United States, the U.S. Coast Guard is responsible for managing and overseeing the AMVER system, including for vessels operating in the Gulf of Mexico. The other answer choices are incorrect because the Corps of Engineers, Minerals Management Service, and Department of Energy do not have the authority or responsibility for administering the AMVER system.