To minimize the costs of storing and purchasing sugar, we need to find the function that describes the total cost. Since the storage costs and reorder costs depend on the lot size, we size as our variable and call it $x.$ Then the total storage cost is equal to the storage cost per item multiplied by the average number of items stored at any time. We assume that the the items are stored at any time. Thus, the total storage cost is

$c_s=(1)()$

$$