A company runs a container application by using Amazon Elastic Kubernetes Service (Amazon EKS). The application includes microservices that manage customers and place orders. The company needs to route incoming requests to the appropriate microservices. Which solution will meet this requirement MOST cost-effectively?

The AWS Load Balancer Controller with an Application Load Balancer (ALB) is the most cost-effective solution. ALBs are designed for HTTP/S traffic, making them ideal for routing requests to microservices based on paths or hostnames, which is a common pattern in containerized applications. The AWS Load Balancer Controller automates the provisioning and management of ALBs for EKS services. Network Load Balancers (NLBs) operate at Layer 4 and are less suitable for HTTP/S routing to microservices, and are generally more expensive for this use case. AWS Lambda is a serverless compute service, not a load balancer, and would introduce unnecessary complexity and cost for routing. Amazon API Gateway is a robust solution for API management but is typically more expensive and feature-rich than what's needed solely for internal microservice routing within EKS.