Notwithstanding the provisions of Sections 59-33-50, 59-67-420 and 59-67-510, the State Department of Education shall have the responsibility for transporting handicapped persons of lawful school age to and from the nearest school in which a handicapped pupil has been duly assigned. Additionally, when a school district is providing classes for handicapped persons between the ages of five and twenty-one years at the same location where classes and programs are provided for handicapped persons under age five and over age twenty-one, and when a cost reduction will result, the Department may enter into a reciprocal agreement with the facility whereby certain handicapped persons between the ages of five and twenty-one years may be transported on buses not owned by the Department and certain handicapped persons under age five and over age twenty-one may be transported on Department owned buses.