The construction, equipment, operation and maintenance of such hospital shall be under the supervision and control of a board who shall constitute a body corporate and be known as the board of trustees of the ………….. university county hospital. The board of trustees shall consist of 7 members, 3 of whom shall be chosen by the board of education of the county, not more than 1 of whom shall be a doctor of medicine, and 3 of whom shall be chosen by the governing board of the university referred to in section 1 hereof, not more than 1 of whom shall be a doctor of medicine. The ranking executive officer of the college of medicine of said university shall be an ex officio member of said board of trustees. The appointed trustees shall serve without salary for such term or terms as the appointing power shall determine at the time of such appointment.