Upon establishment of such lists of producers, the Director of Agriculture shall call meetings of producers in each district, for the purpose of nominating persons to be appointed to the office of commissioner. At each such district meeting for the nomination of members, the director or a representative authorized by him shall preside, and receive nominations, and at the conclusion of each such meeting shall announce the names of the persons nominated at the meetings and the time, the manner and instructions for voting by mail. Thereafter, within 10 days after each such meeting, the director shall mail to all producers ballots for the election of members in the respective districts, with instructions for voting by mail. All votes shall be required to be delivered to the Director of Agriculture or mailed for delivery within 10 days after issuance of ballots by the director.