The drainage board shall secure from a competent engineer, plans, specifications, a route and course, and an estimate of cost of the proposed drain, which when approved and adopted by the board shall be filed with the secretary of the board. In approving the plans and specifications, the drainage board is not limited to the route of the drain described in the petition or the final order of determination. Changes in the approved route and course of the drain must be approved by resolution of the drainage board. The drainage board shall tentatively establish the percentage of the cost of the drain or of the several sections or parts of the drain to be paid by public corporations in each county affected and by this state on account of any state highway, and by the county on account of any county road. The percentage of the cost apportioned to public corporations in each county shall then be apportioned by the drain commissioner among public corporations to be assessed in the county, and that apportionment shall be filed with the secretary of the drainage board. In making the apportionments under this section, there shall be taken into consideration the benefits to accrue to each public corporation and the extent to which each public corporation contributes to the conditions that make the drain necessary. Apportionments against this state shall be based upon benefits and contributions as related solely to the drainage of state highways. Apportionments against the county shall be based upon benefits and contributions as related solely to the drainage of its county roads. Before a tentative apportionment is made, the drainage board shall designate the area to be served by the drain project, which may include all of the area in a public corporation to be assessed, and may divide the drain into sections or parts for purposes of apportionment or construction. Notwithstanding any other provision of this act, a county may assume any additional cost of the drain if 2/3 of the members elect of the county board of commissioners vote in favor thereof. The apportionment under this section applies only to the proposed drain. The apportionments for any extensions or other work subsequently performed under section 535 shall be reestablished by the board. If chapter 25 is employed in the apportionment of costs, the proceedings under this section shall be altered and supplemented as provided in chapter 25.