A company runs containers in a Kubernetes environment in its local data center. The company wants to use Amazon Elastic Kubernetes Service (Amazon EKS) and other AWS managed services. Data must remain on-premises in the company's data center and cannot be stored offsite or in the cloud. Which solution meets these requirements?

Installing an AWS Outposts rack in the company's data center is the correct solution. AWS Outposts extends AWS infrastructure, services, APIs, and tools to virtually any data center, co-location space, or on-premises facility. This allows the company to run Amazon EKS and other AWS managed services locally, ensuring data remains on-premises while leveraging the AWS cloud operating model. Deploying AWS Local Zones is incorrect because Local Zones are extensions of an AWS Region geographically closer to users, not designed for installation within a private data center. Using an AWS Snowmobile is incorrect as it's a large-scale data migration service, not a solution for running persistent AWS services on-premises. Installing an AWS Snowball Edge Storage Optimized node is incorrect because while it offers compute and storage, it's primarily for edge computing and data transfer, not for hosting a full Amazon EKS environment with the full suite of AWS managed services as required.