The department may enter into agreements under sections 39-2808 to 39-2824 to let, design, and construct projects for political subdivisions when any of the funding for such projects is provided by or through the department. In such instances, the department may enter into contracts with the design-builder, progressive design-builder, or construction manager. The provisions of the Political Subdivisions Construction Alternatives Act shall not apply to projects let, designed, and constructed under the supervision of the department pursuant to agreements with political subdivisions under sections 39-2808 to 39-2824.