Final answer:
Support personnel in a line and staff organization provide advice to line managers but do not have direct ordering authority, much like advisors in the Executive Office of the President.
Step-by-step explanation:
In a line and staff organization, those who advise line personnel but do not have the authority to issue direct orders to them are known as the company's support personnel. These individuals are experts in their field and provide specialized knowledge and assistance to help inform the decisions made by line managers.
This structure is reflective of the Executive Office of the President, where staff members, advisors, and bodies like the Council of Economic Advisers and the National Security Council advise the president but do not have the authority to execute orders on their behalf. Moreover, these support staff members serve at the discretion of the president and often assist in making a vast majority of decisions, thereby playing a crucial role in the operation of the administration.