In addition to the duties expressly set forth elsewhere in this article, the board shall:

1. (1) Represent the public interest in the improvement of personnel administration in the classified service.
2. (2) Advise the Governor, the secretary, and the director on problems concerning personnel administration.
3. (3) Foster the interest of institutions of learning and of industrial, civic, professional and employee organizations in the improvement of personnel standards in the classified service.
4. (4) Make any investigation which it may consider desirable concerning the administration of personnel in the classified service and make recommendations to the director with respect thereto.
5. (5) Approve the budget as prepared by the director for administration of this article before submission to the Division of Finance and administration.