Network Function Virtualization (NFV) is a promising solution for telecom operators and service providers to improve business agility, by enabling a fast deployment of new services, and by making it possible for them to cope with the increasing traffic volume and service demand. NFV enables virtualization of network functions that can be deployed as virtual machines on general purpose server hardware in cloud environments, effectively reducing deployment and operational costs. To benefit from the advantages of NFV, virtual network functions (VNFs) need to be provisioned with sufficient resources and perform without impacting network quality of service (QoS). To this end, this paper proposes a model for VNFs placement and provisioning optimization while guaranteeing the latency requirements of the service chains. Our goal is to optimize resource utilization in order to reduce cost satisfying the QoS such as end-to-end latency. We extend a related VNFs placement optimization with a fine-grained latency model including virtualization overhead. The model is evaluated with a simulated network and it provides placement solutions ensuring the required QoS guarantees.