Which of the following is an appropriate treatment option for type 1 diabetes mellitus?

Regular insulin is the appropriate treatment option for type 1 diabetes mellitus because individuals with this condition are unable to produce insulin due to the destruction of pancreatic beta cells, often as a result of an autoimmune process. Insulin therapy is essential for managing blood glucose levels and preventing hyperglycemia in these patients.

Regular insulin is a short-acting form of insulin that can effectively control blood sugar levels after meals. It acts quickly to lower blood glucose, making it crucial for patients who experience rapid increases in blood sugar following food intake. Treatment typically necessitates a combination of basal (long-acting) and bolus (short-acting, such as regular insulin) insulin to mimic the body's normal insulin response to meals and between meals.

The other options listed are more suitable for type 2 diabetes mellitus and are ineffective for treating type 1 diabetes. Glucophage (metformin) and sulfonylureas such as glimepiride work by increasing insulin sensitivity and stimulating insulin secretion from the pancreas, which is not applicable to individuals with type 1 diabetes, as they lack insulin production altogether. Hence, these medications do not provide the necessary management for type 1 diabetes.