The county commission in all counties of class two, by order entered of record, may authorize all county offices, except the sheriff’s office, to be open not more than five days each week, and in all counties of classes three and four by order entered of record, may authorize all county offices, except the sheriff’s office, to be open not more than five and one-half days each week. The county commission, after entering such an order, may require any office to be open six days a week when public convenience requires. The authorization by the county commission in counties of the third and fourth class to close such offices must be published three times in the county newspapers and such authorization to be signed by the county commission.