Binary variables \(y\) (choice of ingredients) and continuous variables \(x\) (wt %) Problem formulation
high spreading emollient: yi,xi                              medium spreading emollient: yj,xj                              low spreading emollient: yk,xk                               thickening polymer: yn,xn                                      fatty alcohol: yi,xi                                          nonionic surfactant: yi,xi  Find vectors \(\mathbf{y}\) and \(\mathbf{x}\) that minimize cost, subject to: Heuristics of typical amounts and combinations of ingredients \(2.0\leq\gamma\leq 2.4\) yn,xn  such that  \(\eta_{1}\ \)and\(\ \eta_{2}\) are within specifications HLB = RHLB