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The 23,000-seat City Coliseum 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. Coliseum vending annually sells large quantities of softdrinks and beer in plastic cups with the name of the coliseum and the various team logos 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($)
2,000-6,999 47
7,000-11,999 43
12,000-19,999 41
20,000 plus 38

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