The correct answer is A) pumping out flooded compartments. Minimizing progressive flooding in the engine room involves securing watertight boundaries and actively pumping out any flooded compartments. This helps prevent the flooding from spreading to other areas of the vessel. The other options are incorrect because: B) Transferring reserve feed water would not directly address the issue of progressive flooding. C) Dumping fuel oil would not stop the flooding itself. D) Evacuating the engine room does not actively mitigate the flooding. Pumping out flooded compartments is the most effective way to minimize progressive flooding and preserve the vessel's watertight integrity.