The evolution of antibiotic resistance in microbes poses one of the greatest challenges to the management of human health. Because addressing the problem experimentally has been difficult, research on strategies to slow the evolution of resistance through the rational use of antibiotics has resorted to mathematical and computational models. However, despite many advances, several questions remain unsettled. Here we present a population model for rational antibiotic usage by adding three key features that have been overlooked: 1) the maximization of the frequency of uninfected patients in the human population rather than the minimization of antibiotic resistance in the bacterial population, 2) the use of cocktails containing antibiotic pairs, and 3) the imposition of tradeoff constraints on bacterial resistance to multiple drugs. Because of tradeoffs, bacterial resistance does not evolve directionally and the system reaches an equilibrium state. When considering the equilibrium frequency of uninfected patients, both cycling and mixing improve upon single-drug treatment strategies. Mixing outperforms optimal cycling regimens. Cocktails further improve upon aforementioned strategies. Moreover, conditions that increase the population frequency of uninfected patients also increase the recovery rate of infected individual patients. Thus, a rational strategy does not necessarily result in a tragedy of the commons because benefits to the individual patient and general public are not in conflict. Our identification of cocktails as the best strategy when tradeoffs between multiple-resistance are operating could also be extended to other host-pathogen systems. Cocktails or other multiple-drug treatments are additionally attractive because they allow re-using antibiotics whose utility has been negated by the evolution of single resistance.