By running nodes in both environments, you can:

1. _Optimize resource utilization_: Utilize cloud resources for scalability and on-premise resources for sensitive data.

2. _Enhance flexibility_: Easily move workloads between cloud and on-premise environments as needed.

3. _Improve disaster recovery_: Use cloud resources for backup and recovery in case of on-premise failures.

4. _Reduce costs_: Leverage cloud resources for variable workloads and on-premise resources for steady workloads.

5. _Increase security_: Use on-premise resources for sensitive data and cloud resources for less sensitive workloads.

6. _Simplify management_: Use cloud management tools for on-premise resources and vice versa.

7. _Support hybrid applications_: Run applications that require both cloud and on-premise resources.

8. _Future-proof infrastructure_: Prepare for future cloud and on-premise innovations and integrations.

To implement a cloud and on-premise mix:

1. _Assess workload requirements_: Determine which workloads are suitable for cloud and on-premise environments.

2. _Choose cloud and on-premise providers_: Select providers that offer hybrid solutions and integrations.

3. _Set up hybrid infrastructure_: Configure nodes in both cloud and on-premise environments.

4. _Develop a management strategy_: Use tools and processes to manage nodes across both environments.

5. _Ensure security and compliance_: Implement security measures and ensure compliance across both environments.

6. _Monitor and optimize performance_: Regularly monitor and optimize node performance in both environments.

7. _Develop a disaster recovery plan_: Create a plan that leverages cloud resources for backup and recovery.

8. _Continuously evaluate and adjust_: Regularly assess and adjust the cloud and on-premise mix as needed.