  The Bergman minimal model is a dynamic model of plasma glucose concentration.
It has two input variables -- insulin delivery and carbohydrate intake. We
investigate the behaviour of plasma glucose concentration predicted by the
model given carbohydrate (CHO) inputs and commensurate insulin inputs. We
observe that to maintain plasma glucose above a specified minimum concentration
results in an unavoidable peak in plasma glucose. Additionally, we specify the
timing and magnitude of a bolus pulse to minimise this unavoidable peak in
plasma glucose concentration whilst attaining but not going below the desired
minimum glucose concentration. Finally, we obtain necessary and sufficient
conditions for the glucose concentration to be minimised.
