If after the bids have been rejected, the board determines and declares by a four-fifths vote of all the members of a five-ward district, or by a five-sevenths vote of all the members of a seven-ward district, that in its opinion the materials and supplies may be purchased at a lower price in the open market, the board may proceed, or may authorize the general manager to proceed, to purchase the supplies and materials in the open market without further observance of the provisions requiring contracts, bids, or notice.