The aqueous tricomponent surfactant mixture dodecyltrimethylammonium bromide (DTAB), sodium 10-undecenoate (SUD), and sodium dodecanoate (SDD) has been studied over the complete triangular diagram. This system is highly nonideal and has a coacervate domain. The mixtures do not precipitate in any proportion. There is a wide region of the phase diagram with positive deviations of the critical micelle concentration (CMC). The thermodynamic analysis has been done with the recently developed equation-oriented mixed micellization model (EOMMM) since the widely employed multicomponent regular solution theory (MRST) failed to represent this subregular ternary surfactant system. The advantages of the EOMMM over the MRST are discussed. The biocide properties of DTAB and SUD against microorganisms, the high CMCs that ensure high concentrations of biologically active monomers, and the possibility of having a system that remains liquid in any proportion make the present system attractive for the design of bactericide and antifungal preparations for the medicine, food, and cosmetic industries.