The 23,000-seat City Coliseum houses the local professional sports teams as well as various trade show, circuses, etc. Coliseum vending annually sells large quantities of soft drinks and beer in plastic cups with the name of the coliseum on them. The local container cup manufacturer that supplies the cups in boxes of 100 has offered coliseum management the following discount price schedule for cups:

Order Quantity (Boxes)	Price Per Box
1-1,499	$48.50
1,500 - 4,999	$47.50
5,000-6,999	$47.25
7,000+	$47.00

The annual demand for cups is 3.0 million (30,000 boxes), the annual carrying cost per box of cups is 35% of the cost of a box, and the ordering cost is $1,000 per order. The total annual inventory cost considers the cost of holding or carrying the inventory, the ordering cost, and th acquisition cost of the products.

a) Determine the optimal order quantity using the appropriate inventory management model. Provide the results you used in making your decision. Assume that the demand is known and constant and the lead time is also known and constant. Replenishment is instantaneous. Also, because of the nature of this operation, no stock outs are allowed.

b) What is the lowest total annual inventory cost (including holding, ordering and acquisition costs) for each "price per box"?