In establishing a jointly owned and operated county nursing home or facility for supportive services, each of the cooperating counties shall determine by a majority vote of the county board that it is in favor of the establishment of the home or of the facility, the place of its location, and the approximate amount to be spent for the establishment of the proposed nursing home or facility. Each county shall authorize the payment by that county of its proportionate share of the cost of the establishment. The proportion of costs of the establishment, and of costs of maintenance and operation of the nursing home or facility to be paid by each county shall be set by terms agreed upon by each of the participating counties.