The correct answer is A, AWS Business Support. This plan is the most cost-effective option that includes programmatic case management through the AWS Support API. It is designed for customers who need more than the basic support but are not ready for the comprehensive features of the AWS Enterprise Support plan. AWS Basic Support (option B) does not offer the API access, AWS Developer Support (option C) also lacks this feature, and while AWS Enterprise Support (option D) does include programmatic case management, it may not be as cost-effective as the Business Support plan for companies with lighter support needs.