In executing a writ of ejectment, the constable or deputy sheriff shall proceed to the premises, present to the occupants a copy of the writ and give the occupants twenty-four hours to vacate voluntarily. If the occupants refuse to vacate within twenty-four hours or the premises appear unoccupied, the constable or deputy sheriff shall announce his identity and purpose. If necessary, the deputy sheriff, but not a constable, may then enter the premises by force, using the least destructive means possible, in order to effectuate the ejectment. If the premises appear to be occupied and the occupant does not respond, the constable or deputy sheriff shall leave a copy of the writ taped or stapled at each corner and attached at the top of either the front or back door or in the most conspicuous place. Twenty-four hours following the posting of the writ, if the occupants have not vacated the premises voluntarily, the deputy sheriff, but not a constable, may then enter the premises by force, using the least destructive means possible, in order to effectuate the ejectment. Discretion may be exercised by the constable or deputy sheriff in granting a delay in the dispossession of ill or elderly tenants.