We present a compartment model that explains melanoma cell response and resistance to mono and combination therapies. Model parameters were estimated by utilizing an optimization algorithm to identify parameters that minimized the difference between predicted cell populations and experimentally measured cell numbers. The model was then validated with in vitro experimental data. Our simulations show that although a specific timing of the combination therapy is effective in controlling tumor cell populations over an extended period of time, the treatment eventually fails. We subsequently predict a more optimal combination therapy that incorporates an additional drug at the right moment.