The accounts of the institutions shall be annually closed and balanced on the first Monday of January in each year. And full reports of the preceding year shall then be made and submitted to the city council and county commissioners, which shall be published as a Class I legal advertisement in compliance with the provisions of article three, chapter fifty-nine of this code, and the publication area for such publication shall be the county; and the city council and county commissioners, or either of such bodies, may require such other reports and exhibits of the condition and management of such institution as they may deem proper.