To adapt to the emerging microservice-based architectures, user application requests are transformed from the traditional service-based monolithic configuration to that of multi-stage inner-dependent microservices. However, in a cloud-edge continuum, the distribution of microservices introduces extra communication overhead that could violate the Service Level Objectives (SLOs). Existing microservice-based resource allocation techniques have either considered only the case that instances belonging to the same microservice are deployed on the same server, or have not considered the case with SLO constraints. In this paper, we consider the case where instances belonging to the same microservice can be deployed across servers with SLO constraints. We propose a novel linear program (LP) based resource configurator to determine the desired number of instances of each microservice that edge servers should resource based on performance estimation for application requests such that the total cost of allocated resources of all needed microservices is minimized under the constraint that the maximum microservice completion time satisfies the given service level objective (SLO). We prove that our resource configurator achieves the worst-case performance guarantee (√2 + 1)2 by rigorous derivation. In comparison with the state-of-the-art microservice allocation methods, experimental results show that our proposed resource configurator reduces the computational resource usage by 7.6%, and the memory resources by 11.3% while guaranteeing the SLOs.