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Joint optimization of electric vehicle (EV) fast charging and DC fast charging (DCFC) station problems is presented in this paper. An electro-thermal-aging model is used for modeling EV's battery cell. The model is then expanded from a single cell to a battery pack based on the structure of commercially available EV batteries in the market. Moreover, the limitations imposed by the DCFC station are properly considered in the problem's constraints, including restrictions due to the cost of electricity, especially demand charge, and port power rating of chargers. The station's profit is maximized, and its cost is minimized considering demand charge and energy charge tariffs. Finally, the problem is discretized and numerically evaluated in a detailed case study.