A hospital needs $3,100$ units of a medicine throughout the year. The purchasing cost varies with the size of the order. If the number of units of the medicine that the hospital orders is below $100,$ the supplier charges $$30$ per unit; if it is between $100$ and $499,$ the price is $$27$ each; and if they order $500$ units and above, it is $$26$ per unit. The holding cost per unit per year is $$30,$ as the medicine must be kept in a special device to prevent spoilage. The ordering cost is $$10.$ a$.$ How many units of the medicine can hospital order each time to minimize their total cost? $($Round your answer to a whole number.$)$ b$.$ What is the minimum annual total cost? $($Round your answer to a whole number.$)$