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The Lily Hat Shop Limited counted the entire inventory in its store on August $31$ and arrived at a total inventory cost of $$85,600.$ The count included $$7,700$ of inventory held on consignment for a local designer; $$470$ of inventory that was being held for customers who were deciding if they actually wanted to purchase the merchandise; and $$1,000$ of inventory that had been sold to customers but was being held for alterations. There were two shipments of inventory received on September $1.$ The first shipment cost $$4,800.$ It had been shipped on August $29,$ terms FOB destination. The second shipment cost $$4,650,$ plus freight charges of $$270.$ It had been shipped on August $28,$ terms FOB shipping point. Neither of these shipments was included in the August $31$ count.

Calculate the correct cost of the inventory on August $31.$

Inventory cost $