Advances in deep neural networks (DNNs) have significantly contributed to the development of real-time video processing applications. Efficient scheduling of DNN workloads in cloud-hosted inference systems is crucial to minimizing serving costs while meeting application latency constraints. However, existing systems suffer from excessive module latency during request dispatching, low execution throughput during module scheduling, and wasted latency budget during latency splitting for multi-DNN application, which undermines their capability to minimize the serving cost. In this paper, we design a DNN inference system called Harpagon, which minimizes the serving cost under latency constraints with a three-level design. It first maximizes the batch collection rate with a batch-aware request dispatch policy to minimize the module latency. It then maximizes the module throughput with multi-tuple configurations and proper amount of dummy requests. It also carefully splits the end-to-end latency into per-module latency budget to minimize the total serving cost for multi-DNN applications. Evaluation shows that Harpagon outperforms the state of the art by 1.49 to 2.37 times in serving cost while satisfying the latency objectives. Additionally, compared to the optimal solution using brute force search, Harpagon derives the lower bound of serving cost for 91.5% workloads with millisecond level runtime.