This study considers the reverse multi-attribute, or procurement auction in which the item for sale is defined by several quality attributes in addition to the price, the buyer is the auctioneer, and the sellers are the bidders. We focus on a variation of the first-price sealed-bid protocol termed first-score sealed-bid auction. We analyze a specific model for the protocol, and we provide optimal strategies for both the auctioneer and the bidders participating in the auctions. In addition, we conclude that the auctioneer can manipulate the auction to yield better outcome, however, as the number of the bidders participating in the auction increases, the buyer is motivated to announce a real utility function.