Only after notice is published once a week for four weeks in the official organs of all the counties bordering Lake Lanier and in the official organ of Fulton County, the property described in this part shall be leased as deemed appropriate by the authority at public auction or by sealed competitive bids. The authority shall have the privilege of setting minimum prices below which no bid for lease shall be accepted. When in the opinion of the authority the public welfare demands it, the authority may conclude any authorized lease by private negotiation after first giving notice to the Attorney General of the particulars.