The socioeconomic impact of cloud solutions and particularly PaaS (platform as a service) solutions is becoming increasingly critical. The main objective of PaaS providers is to generate the maximum profit from the services they provide. This requires them to face a number of challenges such as efficiently managing the underlying resources and satisfying the SLAs of the hosted applications. In this paper, we consider a cloud-bursting PaaS environment where the PaaS provider owns some private resources and is able to rent public cloud resources on demand. In that context, we propose a profit-efficient solution for managing such a system under SLA constraints. We define a profit optimization policy that evaluates the cost of hosting each application using public and private resources and chooses the option that generates the highest profit. During peak periods, the optimization policy considers two more options. The first option is to obtain some resources from running applications, taking into account the payment of penalties if their promised quality of service is affected. The second option is to wait until private resources become available, taking into account the payment of penalties if the quality of service promised to the new application is affected. Furthermore, we designed and implemented an open cloud-bursting PaaS system, called Meryn, which integrates the proposed optimization policy and provides support for batch and MapReduce applications. The results of our evaluation show the effectiveness of our approach in optimizing the provider profit. Indeed, compared to a basic approach, our approach provides up to 11.59% and 9.02% more provider profit in, respectively, simulations and experiments.