The collection and transportation of trash and waste materials shall be at all times under the general supervision of the Mayor or his or her duly authorized agent, who shall have the authority by and with the consent of the Governing Body to make additional rules and regulations not inconsistent with the terms and provisions of this article requiring that the collection and transportation of trash and waste materials shall be conducted in such manner as not to endanger the public health, or to become an annoyance to the inhabitants of the city, and providing for a proper fee to be charged to the customer.