After the tentative apportionments of costs have been made, the board shall set a time, date, and place it will meet and hear objections to the apportionments. Notice of the hearing shall be published twice in each county involved by inserting the notice in at least 1 newspaper designated by the board and published in the county. The first publication is to be not less than 20 days before the time of hearing. The notice shall also be sent by registered mail to the clerk or secretary of each public corporation proposed to be assessed, except that a notice to the state shall be sent to the state highway director and the director of the department of natural resources and a notice to a county shall be sent both to the county clerk and the county road commission. The mailing shall be made not less than 20 days before the time of the hearing. The notice shall be signed by the secretary and proof of the publication and mailing of the notice shall be filed with the secretary. The board may provide a form to be substantially followed in the giving of the notice. The notice shall include tentative apportionments to the several public corporations. After the hearing, the board shall make a written report of its findings on the apportionments to the commission, which may either confirm the apportionments as tentatively made or may recommend readjustments of any apportionments considered inequitable.