In this paper we have used the Glucose-Insulin-Glucagon mathematical model proposed in [2–4], which describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes and designed an optimal dosing schedule of either insulin or insulin and glucagon together to regulate the blood glucose index (BGI), while limiting the total amount of insulin and glucagon administered. Here, INS is linked to type 1 diabetes mellitus.