Within 120 days of all members being appointed, the districting commission shall adopt a plan to apportion the county into five single-member districts. The apportionment plan hereinafter referred to as plan, shall be submitted to the board, commission, and delegation within 10 days after adoption. Unless the plan is rejected by resolution of each of the three appointing authorities within 35 days after the plan is adopted by the districting commission or unless the plan is superseded by legislative act, the plan becomes final. If the plan is rejected by a resolution of each of the appointing authorities, the districting commission shall submit, within 30 days, an additional plan for consideration. Once the plan becomes final, the districting commission shall cease to function. The plan shall be effective for the election of the members of the commission at the time of the next election for any member of the commission. The plan shall be effective for the election of the members of the board at the time of the next election for any member of the board.