Suppose that the demand for a product is 30 units per month and the items are withdrawn at a constant rate. The setup cost each time a production run is undertaken to replenish inventory is $15. The production cost is $1 per item, and the inventory holding cost is $0.30 per item per month.
(a) Assuming shortages are not allowed, determine how often to make a production run and what size it should be.
(b) If shortages are allowed but cost $3 per item per month, determine how often to make a production run and what size it should be.