The commissioner shall issue an order to the client or the guardian of the estate, if there be one, and relatives determined able to pay requiring them to pay to the state of Minnesota the amounts so determined the total of which shall not exceed the full cost of care. Such order shall specifically state the commissioner’s determination and shall be conclusive unless appealed from as herein provided. When a client or relative fails to pay the amount due hereunder the attorney general, upon request of the commissioner, may institute, or direct the appropriate county attorney to institute, civil action to recover such amount.