The board of supervisors of any county now or hereafter having a population of 500,000 or more as determined by the last federal decennial census or by any federal decennial census hereafter taken in which there is or may be located a publicly owned university having a college of medicine may appropriate not to exceed $2,000,000.00 for the purpose of defraying the cost of constructing and equipping a university county hospital for teaching and research. The size of said hospital shall not exceed 350 beds and the services of said hospital shall be limited to indigent patients.