Final answer:
The condition where the pancreas cannot produce insulin due to the destruction of beta islet cells is known as Diabetes mellitus Type 1, an autoimmune disease requiring synthetic insulin administration.
Step-by-step explanation:
When the pancreas is unable to produce insulin because autoimmune, genetic, or environmental factors have destroyed the beta islet cells, the condition is known as Diabetes mellitus Type 1. This is an autoimmune disease where the person's immune system attacks the insulin-secreting beta cells within the pancreas. Unlike Type 2 diabetes, which involves a combination of insulin resistance and impaired insulin secretion, Type 1 diabetes occurs when the beta cells are completely destroyed, leading to a complete lack of insulin production. As a result, individuals with this condition must rely on synthetic insulin administration to control blood glucose levels.