Large Language Models have transformed the Contact Center industry, manifesting in enhanced self-service tools, streamlined administrative processes, and augmented agent productivity. This paper delineates our system that automates call driver generation, which serves as the foundation for tasks such as topic modeling, incoming call classification, trend detection, and FAQ generation, delivering actionable insights for contact center agents and administrators to consume. We present a cost-efficient LLM system design, with 1) a comprehensive evaluation of proprietary, open-weight, and fine-tuned models and 2) cost-efficient strategies, and 3) the corresponding cost analysis when deployed in production environments.