Sec. 19. Following the hearing the county executive may authorize the execution of the lease originally agreed on or make modifications agreed on with the authority, the governing board, and the county fiscal body. The authorization must be by an order entered in the official records of the county executive. The lease shall be executed:
(1) on behalf of the county by at least a majority of the members of the county executive; and
(2) on behalf of the authority by the president or vice president and secretary of the governing board of the authority.