A county milk commission shall consist of six members who reside in the county where the commission is located and who shall be appointed by the board of supervisors for a term of four years and shall be eligible for reappointment. The members shall be appointed as follows:

1. (a) A physician who is a member of a county medical association organized under and approved by the Medical Society of the State of California.
2. (b) A physician nominated by the county health department.
3. (c) A veterinarian, who shall be a member of the county or regional veterinarian association.
4. (d) A physician nominated by a producer or producers of certified milk in the county.
5. (e) A physician nominated by the American Association of Medical Milk Commissions, Incorporated.

6. (f) A public member, appointed by the board of supervisors.

   If no nomination is made by a group so authorized to nominate a member under subdivisions (a) to (e), inclusive, the board of supervisors shall appoint a person who is a member of any of the designated organizations authorized to nominate members.