Edge cloud technologies enable faster and more energy-efficient processing of user requests on servers located at the network's edge. However, when compared to the cloud, edge resources are significantly more limited, prompting a critical question: as user requests arrive, how to determine which ones to allocate to the edge and which ones to the cloud. Additionally, to ensure a quality of service that considers task priorities, it is essential to reserve available resources for potential high-priority requests. This introduces a fundamental trade-off: reserving excessive computing resources at the edge, in anticipation of high-priority requests, is incompatible with reducing energy consumption. Conversely, allocating all edge resources may push higher-priority, potentially more delay-sensitive tasks into the cloud. To tackle this intricate problem, we present a multi-objective reinforcement learning approach utilizing a modified Q-learning process. This approach facilitates intelligent resource allocation, striking a careful balance between fulfilling high-priority requests and minimizing unused processing capacity. While the multi-objective agent ensures the satisfaction of high-priority services, it optimally utilizes the edge resources. Additionally, we introduce a framework for adapting the two cost components to specific requirements, favoring one objective over the other, and examining their impact on relevant metrics. Results demonstrate that this specialized strategy outperforms a conventional First Come First Served baseline, as well as a myopic strategy, which represents the unmodified Q-learning process, across these metrics.