It shall be the duty of the authorized city official to supervise construction or repair of sidewalks within the city. He shall cause specifications to be prepared for the construction of the various kinds of pavements and transmit the Mayor for approval. When the specifications are approved, the Mayor shall advertise for proposals to do all the work which may be ordered by the city in construction and repair of sidewalks, and shall contract therefor for a period not exceeding one year, with the lowest responsible bidder, who shall furnish good and sufficient sureties for the faithful performance of the work. The Mayor may make separate contracts for the different kinds of work with different parties.