Ventilation is at the origin of a spending of energy coming from air circulation in the bronchial tree and from the mechanical resistance of the tissue to motion. Both amplitude and frequency of ventilation are submitted to a trade-off related to this energy, but they are also submitted to a constraint linked to the function of the lung: to transport enough oxygen and carbon dioxide in order to respect metabolism needs. We propose a model for oxygen and carbon dioxide transport in the lung that accounts for the core physical phenomena: lung's tree-like geometry, transport of gas by convection and diffusion, exchanges with blood and a sinusoidal ventilation. Then we optimize the power dissipated by the ventilation of our model relatively to ventilation amplitude and period under gas flow constraints. Our model is able to predict physiological ventilation properties and brings interesting insights on the robustness of different regimes. Hence, at rest, the power dissipated depends very little on the period near the optimal value. Whereas, at strong exercise any shift from the optimal has dramatic effect on the power. These results are fully coherent with the physiological observation and raises the question: how the control of ventilation could select for the optimal configuration? Also, interesting insights about pathologies affecting ventilation could be derived, and our model might give insights on therapeutical responses, with specific breathing strategies or for better driving mechanical ventilation.