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An increasing renewable energy sources (RES) penetration in the recent years has also increased the need for additional flexibility sources and technologies that increase the RES utilization. In addition to battery energy storage, electrolyzers, a technology that produces hydrogen without emitting CO$_{;2};$, are also receiving an increasing attention. This paper proposes a bi- level profit maximization model for a large battery-electrolyzer facility operation in the day-ahead electricity market. The upper level maximizes the overall profit of the facility, while the lower level simulates the market clearing by maximizing the social welfare. The proposed model is tested on the IEEE RTS-24 test system expanded with wind farms to replicate a modern power system. The presented case study shows how different levels of installed power capacity affect the obtained profit and discusses the battery and electrolyzer utilization.