Final answer:
The personnel controlling equipment in theatrical productions are the technical director, master electrician, and master carpenter, while in military logistics it would involve appointed leaders and engineers.
Step-by-step explanation:
The personnel who control the equipment by directing the folks in the transportation control unit can vary depending on the context. In the context of theater production, key personnel include the technical director, the master electrician, and the master carpenter. The technical director oversees set building and safety, the master electrician is in charge of lighting, and the master carpenter ensures the set operates safely. In a military or logistical setting, such as during the U.S. Railroad Administration era or in military engineering, personnel would include various ranks of officers and engineers who are responsible for directing transport and logistical operations. In the example of the U.S. Railroad Administration, an appointed leader such as William McAdoo would have overall control, with support personnel handling specific aspects of transportation.