To the extent allowed under 49 U.S.C. Sec. 14501, the commission shall: Supervise and regulate every contract carrier in this state; fix, alter, and amend, just, fair, and reasonable classifications, rules, and regulations and minimum rates and charges of each contract carrier; regulate the account, service, and safety of contract carriers' operations; require the filing of reports and of other data thereby; and supervise and regulate contract carriers in all other matters affecting their relationship with both the shipping and the general public.