The county commission, township board and special road district of any county declared a noxious weed control area, in addition to any and all taxing powers which it may possess, may levy upon all property subject to its authority a tax in an amount not to exceed fifteen cents on each one hundred dollars assessed valuation, for the purpose of paying the expenses of the county weed control board or the agent of the board in making the inspection required under the provisions of section 263.456, and for the expense of controlling noxious weeds on county roads, rights-of-way, and at other places where noxious weeds may be found. All of the cost of control of noxious weeds on all lands and highways owned or supervised by the department of transportation shall be paid by the department of transportation out of funds appropriated for its use, and the county commission may share costs pursuant to contract with the landowners of property where noxious weeds may be found.