The members of said board shall meet at some place to be agreed upon by the trustees appointed within ten days after their appointments have been made and organize by electing one of their members president, and one vice president, a treasurer and a secretary which position they shall hold for two years. They shall elect such other officers as they deem necessary. They shall make and adopt such bylaws, rules and regulations for the management of such hospitals and the admission and discharge of patients as they shall deem expedient. A majority of the board shall constitute a quorum for business.