Which of the following use cases is suitable for AWS Lambda@Edge?

Using AWS Lambda@Edge for image optimization at edge locations is highly suitable due to its unique capabilities. Lambda@Edge allows for the execution of serverless functions closer to the user's location, specifically at AWS edge locations associated with the Amazon CloudFront content delivery network. This proximity reduces latency and enhances user experience by allowing faster image delivery and optimization as content is being served.

In the context of image optimization, Lambda@Edge can dynamically resize images, convert formats, or apply compression based on the user's device and viewport. This means that images can be optimized in real-time as requests are made, providing a better user experience with quicker load times and reduced bandwidth usage.

The other mentioned use cases are not ideal for Lambda@Edge due to their nature. Running long-term database migrations, data warehousing tasks, and batch processing typically require significant compute resources and may involve extensive processing times that are not suited for the event-driven nature of Lambda@Edge. These tasks are better suited to AWS services that are designed for compute-intensive processes, such as AWS Lambda for serverless applications, Amazon EC2 for virtual servers, or Amazon EMR for big data processing.