Which Microsoft Azure load balancing option supports UDP when the client has a hard-coded IP address for the hostname?

The Azure Load Balancer is the correct choice because it is specifically designed to handle both TCP and UDP traffic, making it suitable for scenarios where applications use these protocols for communication. In situations where the client relies on a hard-coded IP address for the hostname, the Azure Load Balancer can effectively distribute incoming UDP traffic across multiple backend instances, ensuring high availability and reliability for services that use User Datagram Protocol.

This capability is particularly important for applications that require real-time data transfer and do not need the connection-oriented features found in TCP. The Azure Load Balancer's ability to manage UDP traffic seamlessly allows for a consistent user experience, especially in applications like gaming, VoIP, or video streaming.

Other options, such as the Application Gateway, are primarily focused on HTTP/HTTPS traffic and do not support UDP. Traffic Shaper typically deals with bandwidth management rather than load balancing, and Azure DNS Balancer is more about DNS resolution and does not directly manage traffic distribution for UDP. Thus, the Azure Load Balancer stands out as the ideal solution for the described scenario.