The procurement of supplies is often conducted through the buyer analogue of an auction. Sealed bids are submitted and the contract is awarded to the lowest bidder. Although this method may be an optimal way of selling an object, an additional complication arises in the case of purchasing a good. When sellers are privately informed about the quality of the good to be sold, these mechanisms typically result in the provision of the lowest quality object. This paper characterizes optimal mechanisms in environments where sellers are privately informed about quality. It shows that the commonly used auction mechanism is privately or socially optimal in only a small class of environments. In another plausible set of environments the optimal mechanism is simply to order potential supplies and to tender take-it-or-leave-it offers to each sequentially. We use the duality theorem of linear programming to provide a methodology by which necessary and sufficient conditions can be derived to determine when any incentive compatible trading environment maximizes social or private surplus.