Final answer:
The first method to resolve the problem is to follow the chain of command.
Step-by-step explanation:
The first method that should be used to resolve the problem when fraud, waste, or other violations exist within a command and the commanding officer and key management officials are aware of the problem but do nothing is to follow the chain of command. Following the chain of command means reporting the issue to your immediate supervisor or a higher-ranking official within the organization. This allows for the problem to be addressed internally and potentially resolved without causing further conflict or damage to your own reputation.