If it is found that the maximum amount established by the board of supervisors of the county is insufficient to pay the whole expense of support and maintenance of a ward, dependent child, or other minor person, the court may order and direct that such additional amount as is necessary shall be paid out of the earnings, property, or estate of such ward, dependent child, or other minor person, or by the parents or guardian of such ward, dependent child, or other minor person, or by any other person liable for his support and maintenance, to the county officers designated by the board of supervisors who shall in turn pay it to the person, association, or institution that, under court order, is caring for and maintaining such ward, dependent child, or other minor person.