Final answer:
The Maintenance supervisor is responsible for ensuring equipment tag out in a repair facility to ensure the safety of repair personnel and equipment.
Step-by-step explanation:
The individual responsible for representing the repair facility and ensuring that equipment tag out is completed properly to guarantee the safety of repair and tended personnel is the Maintenance supervisor. Tagging out equipment is a crucial safety procedure where equipment is marked with a tag to indicate that it should not be operated until the tag is removed. This process is designed to prevent accidents and injuries by clearly communicating that the equipment is under maintenance or repair.