The management and direction of such work farms, factories or shops and of the convicted persons sentenced thereto, subject to the periodical visitations of the state authorities at their discretion, shall be under the authority of a non-partisan commission to be elected for that purpose by the board of supervisors of such county. Said board of commissioners shall consist of 3 members. The first 3 members shall be elected by the board of supervisors, at any meeting at which a majority of the members-elect shall decide to operate under this act, as follows: One member for 1 year from and after January first, following this election, 1 for 2 years, 1 for 3 years, after said January first; and annually thereafter at the regular January meeting 1 member shall be elected for the full term of 3 years. Vacancies shall be filled by said board of supervisors. The first commissioners shall assume their duties immediately on election. The commissioners shall be residents of the county which they serve, but no member of the board of supervisors shall be eligible during the term for which he was elected supervisor. The commissioners shall make and subscribe the constitutional oath of office and file the same with the county clerk before assuming their duties.