The commission, on the petition of twenty or more residents of the state engaged in any particular occupation, shall cause an investigation to be made of the wages being paid to minors in that occupation to ascertain whether any substantial number of minors in the occupation are receiving oppressive and unreasonable wages as defined in section 23-311. If, on the basis of information in the possession of the commission, with or without a special investigation, the commission is of the opinion that a substantial number of minors in any occupation or occupations are receiving oppressive and unreasonable wages as defined in section 23-311, it shall appoint a wage board, as described in section 23-314, to report upon the establishment of minimum fair wage rates for minors in such occupation or occupations.