A seller has a single unit of a good to sell to a group of N  bidders. The bidders have a pure common value that is drawn from a  prior distribution that is commonly known, but the seller does not  know the bidders' beliefs about the value. The seller has a  non-negative cost of production, so that the gains from trade can  sometimes be negative. The seller values each auction mechanism  according to the lowest expected profit across all Bayes Nash  equilibria and across all common-prior type spaces that are  consistent with the given known distribution of the value. We  characterize and construct optimal auctions for such a seller. We  report a number of further results on optimal auction design with  common values and maxmin auction design.