It shall be the duty of the Mayor to act as chief conservator of the peace within the City; to supervise the administration of the affairs of the City; to see that all ordinances of the City are enforced; to recommend to the Council for adoption such measures as he may deem necessary or expedient and to keep the Council advised of the financial condition and future needs of the City.  He shall sign on behalf of the City all contracts, conveyances, evidences of indebtedness and all other instruments not otherwise provided by this Charter or by ordinance of Council to be signed on behalf of the City by another official.  He shall exercise such other powers and perform such other duties as are conferred or required by this Charter, by any resolution of the Council or by the General Laws of Ohio.