Pharmacokinetics describes the movement and processing of a drug in a body, while Pharmacodynamics describes the drug's effect on a given subject. Pharmacokinetic/Pharmacodynamic(Pk/Pd) models have become a fundamental tool when predicting bacterial behavior and drug development. In November of 2009, Katsube et al. published their paper detailing their Pk/Pd model for the drug Doripenem and the bacteria P. aeruginosa. In their paper, they determined that there is a dependent relationship between the drug's effectiveness and the dosing strategy of the drug. Therefore, this thesis has applied optimal control in order to optimize the drug's effectiveness, while not burdening the subject with the side effects of the drug. Optimal Control is a mathematical tool used to balance two competing factors. As a result, it has become a useful tool used to make decisions involving complex behavior. By using Optimal Control, the model will maximize the drug's effect on the bacterial population of P. aeruginosa, while minimizing the drug concentration of Doripenem. In doing so, our research will enable doctors and clinicians to maximize a drug's effectiveness on the body, while minimizing side effects.