The council may, in its discretion, direct the finance officer to advertise for bids for construction of all, or part of the improvement project on the basis of the council-approved city manager’s report and before the passage of the ordinance, or after the passage of the ordinance and before the public hearing on the proposed improvement, or at a time after the public hearing – provided, however, that no contract shall be let until after the public hearing has been held to hear objections to the proposed improvement. In the event that part of the work of the improvement is to be done under contract bids, then the council shall determine the time and manner of advertisement for bids and the contracts shall be let to the lowest responsible bidder – provided that the council shall have the right to reject all bids when they are deemed unreasonable or unsatisfactory. The city shall provide for the bonding of all contractors for the faithful performance of a contract let under its authority, and the provisions thereof in case of default shall be enforced by action in the name of the city.