The cockroach is one of the world’s most prolific and resilient pests, with over 3,500 species worldwide. It is important to understand the growth and adaptive mechanisms of cockroach colonies in order to safely control these populations. We present a continuous time, age-structured population model of the Blattella germanica cockroach that includes the application of pesticides and the development of resistant subpopulations. The resulting system of differential equations is then used to optimize treatment strategies using analytical and heuristic optimization techniques. While the model shows that the roach-free equilibrium is always unstable, the strategic application of pesticides can keep populations low, even when a drug-resistant subpopulation develops.