Systematic approaches for the design of mixtures, based on a computer-aided mixture/blend design (CAMbD) framework, have the potential to deliver better products and processes. In most existing methodologies the number of mixture ingredients is fixed (usually a binary mixture) and the identity of at least one compound is chosen from a given set of candidate molecules. A novel CAMbD methodology is presented for formulating the general mixture design problem where the number, identity and composition of mixture constituents are optimized simultaneously. To this end, generalized disjunctive programming is integrated into the CAMbD framework to formulate the discrete choices. This generic methodology is applied to a case study to find an optimal solvent mixture that maximizes the solubility of ibuprofen. The best performance in this case study is obtained with a solvent mixture, showing the benefit of using mixtures instead of pure solvents to attain enhanced behavior.