mcp-solver

# Network Monitoring (Simplified) A company needs to place monitoring software on servers to ensure all network connections are monitored. Each server has a cost and monitoring value. ## Network Structure ### Servers (6 total) | Server | Type | Value | Cost | |--------|------|-------|------| | Core1 | Core | 10 | 3 | | Core2 | Core | 10 | 3 | | Web1 | Web | 6 | 2 | | Web2 | Web | 6 | 2 | | DB1 | Database | 8 | 3 | | Edge1 | Edge | 5 | 1 | ### Network Connections (8 edges) - Core1 connects to: Core2, Web1, DB1 - Core2 connects to: Web2, DB1, Edge1 - Web1 connects to: Web2 - Web2 connects to: Edge1 ## Constraints ### Hard Constraints 1. **Edge Coverage**: Every network connection must be monitored by at least one server on either end 2. **Critical Server**: At least one Core server (Core1 or Core2) must have monitoring ### Soft Constraints 1. **Cost Minimization**: Minimize total deployment cost (weight = cost) 2. **Value Maximization**: Maximize monitoring value (weight = 20 - value) ## Task Find the optimal set of servers to monitor that: - Covers all network connections - Includes at least one Core server - Balances cost and value ## Expected Output - List of servers selected for monitoring - Total cost - Total monitoring value - Verification that all edges are covered