The authority shall act upon all appeals of decisions made by the executive director thereof and shall, upon such appeals, approve or disapprove such administrative actions as may be taken by him. The form of an appeal to the full authority from an action or recommendation of the executive director thereof shall be a written communication from the executive head of the agency or agencies involved to the chairman of the authority, stating the objection and a request to appear before the full authority to present the case in point, on which appeal the authority shall take such action as is indicated by the facts presented to or made available to the authority.