It shall be the duty of the governing body of the county or city within the boundaries of which any work is performed under the provisions of this chapter to allow and order payment at the end of each calendar month, out of the current funds of the county or city, to the Department of Social Services for the support of the prisoner’s spouse or child or children, a sum not less than $20 nor more than $40 for each week in the discretion of the court during any part of which any work is so performed by such prisoner.