A business sells an item at a constant rate of r units per month. It reorders in batches of q units, at a cost of a + bq dollars per order. Storage costs are k dollars per item per month, and, on average, q∕2 items are in storage, waiting to be sold. [Assume r, a, b, k are positive constants.]
(a) How often does the business reorder?
(b) What is the average monthly cost of reordering?
(c) What is the total monthly cost, C, of ordering and storage?
(d) Obtain Wilson’s lot size formula, the optimal batch size which minimizes cost.