Determine the optimal order quantity and total annual inventory cost for cups in Problem 13.33 if the carrying cost is 5% of the price of a box of cups.

Data in Problem 13.33

The 21,000-seat Air East Arena houses the local professional ice hockey, basketball, indoor soccer, and arena football teams as well as various trade shows, wrestling and boxing matches, tractor pulls, and circuses. Arena vending annually sells large quantities of soft drinks and beer in plastic cups with the name of the arena and the various team logos on them. The local container cup manufacturer that supplies the cups in boxes of 100 has offered arena management the following discount price schedule for cups: 

The annual demand for cups is 2.3 million, the annual carrying cost per box of cups is $1.90, and ordering cost is $320. Determine the optimal order quantity and total annual inventory cost.

Order Quantity (Boxes) 2,000-6,999 7,000-11,999 12,000-19,999 20,000+ Price per Box $47 43 41 38