Network Functions Virtualization (NFV) enables carriers to replace dedicated middleboxes with Virtual Network Functions (VNFs) consolidated on a few shared servers. However, the question of how (and even whether) one can achieve performance related Service Level Objectives (SLOs) with software packet processing in NFV remains open. VNF consolidation causes high variability and unpredictability in throughput and latency of VNFs deployed together. It was shown in our prior work that isolating the processor's Last Level Cache (LLC) and limiting Memory Bandwidth (MB) directly helps in achieving performance isolation among the co-located VNFs. So, in this work, we formulate VNF placement problem with exclusive allocation of LLC and MB resources as a Mixed Integer Linear Program (MILP). Due to its hardness to solve, we also present a heuristic solution named RAVIN that enforces performance SLOs for multi-tenant NFV servers while being as much resource-efficient as possible. We demonstrate RAVIN's effectiveness in improving resource utilization and in reducing the total number of required servers to deploy VNFs compared to state-of-the-art and baseline approaches. © 2023 IEEE.