Upon determination of need for or lack of need for a marking of the boundary, the Attorney General of this State shall certify the determination made to the person, firm, or corporation giving notice, and issue a permit that the work upon such alteration, improvement, building, dam, structure, or operation affecting the waters or flow of such river may be begun upon a day certain. Such date shall be fixed as will give a reasonable time for the erection of monuments for the marking of the boundary if a need for such monuments has been determined; otherwise, so as to inconvenience the giver of the notice as little as possible.