Altira Corporation provides the following information related to its inventory during the month of August $2024$ :

August $1$ Inventory on hand $-3,200$ units; cost $$7\mathrm{.}30$ each.

August $8$ Purchased $16,000$ units for $$6\mathrm{.}70$ each.

August $14$ sold $12,800$ units for $$13\mathrm{.}20$ each.

August $18$ Purchased $9,600$ units for $$6\mathrm{.}20$ each.

August $25$ Sold $11,800$ units for $$12\mathrm{.}20$ each.

August $28$ Purchased $5,280$ units for $$5\mathrm{.}80$ each.

August $31$ Inveritory on hand $9,400$ units.

Using calculations based on a perpetual inventory system, determine the inventory balance Altira would report in its August $31,2024.$

balance sheet and the cost of goods sold it would report in its August $2024$ income statement using last$-$in$,$ first$-$out $($LIFO$).$