This paper presents a new extremal approach to deriving dual optimization problems with proper duality inequality which simplifies, and generalizes the Fenchel-Rockafellar scheme. Our derivation proceeds in two stages, (i) inequality attainment,(ii) decoupling primal and dual variables, The power and convenience of this approach are exhibited through a new, much simpler derivation of the Charnes-Cooper results for Khinchin-Kullback-Leibler statistical estimation [1], the immediate establishment of the C2duality for general distributions and its extensions to general linear inequality constraints, plus the development of a new two-person zero-sum game connection.