Upon the request of any county by its board of supervisors, the department shall conduct such studies as are requested, and at the expense of such county, but limited to the county making the request. Such studies shall be made to determine the nature, extent, distribution and sources of air pollution within such county and the possible methods of control and abatement of such pollution within the county making the request. In the conduct of such requested studies the department may seek cooperative arrangements with state universities and other educational institutions of the state, or with other state departments, the county, municipalities or private agencies of any kind which have available facilities or personnel, or both, suitable for the conduct of one or more areas of such research, under the supervision of the department.