In recent years, mobile applications have proliferated across domains such as E-banking, Augmented Reality, E-Transportation, and E-Healthcare. These applications are often built using microservices, an architectural style where the application is composed of independently deployable services focusing on specific functionalities. Mobile devices cannot process these microservices locally, so traditionally, cloud-based frameworks using cost-efficient Virtual Machines (VMs) and edge servers have been used to offload these tasks. However, cloud frameworks suffer from extended boot times and high transmission overhead, while edge servers have limited computational resources. To overcome these challenges, this study introduces a Microservices Container-Based Mobile Edge Cloud Computing (MCBMEC) environment and proposes an innovative framework, Optimization Task Scheduling and Computational Offloading with Cost Awareness (OTSCOCA). This framework addresses Resource Matching, Task Sequencing, and Task Scheduling to enhance server utilization, reduce service latency, and improve service bootup times. Empirical results validate the efficacy of MCBMEC and OTSCOCA, demonstrating significant improvements in server efficiency, reduced service latency, faster service bootup times, and notable cost savings. These outcomes underscore the pivotal role of these methodologies in advancing mobile edge computing applications amidst the challenges of edge server limitations and traditional cloud-based approaches.