Public improvements may be made by the City government itself or by contract. The Council shall award all contracts for such improvements; provided that the Council may authorize the City Manager to award such contracts not exceeding an amount to be determined by the Council, and subject to such regulations as the Council may prescribe. Every contract for public improvements of such amount as the Council may determine by ordinance, or such amount as may be required by the Oklahoma Public Competitive Bidding Act, whichever amount is greater, shall be awarded to the lowest and best responsible bidder after such notice and opportunity for competitive bidding as the Council may prescribe, or as is required by law. All bids may be rejected and further notice and opportunity for competitive bidding may be given. Such contracts may be altered by mutual consent of the parties. Public improvement means any beneficial or valuable change or addition, betterment, enhancement, or amelioration of or upon any real property, or interest therein, belonging to the City, its public trusts or agencies and intended to enhance its value, beauty, or utility, or to adopt it to new or future purposes. The term does not include the direct purchase of materials, equipment, or supplies by the City, its public trusts or agencies. Nothing herein shall prevent the City from constructing public improvements by the force account method.