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

August $1$ Inventory on hand$-3,800$ units; cost $$7\mathrm{.}90$ each.

August $8$ Purchased $19,000$ units for $$7\mathrm{.}30$ each.

August $14$ Sold $15,200$ units for $$13\mathrm{.}80$ each.

August $18$ Purchased $11,400$ units for $$6\mathrm{.}80$ each.

August $25$ Sold $14,200$ units for $$12\mathrm{.}80$ each.

August $28$ Purchased $5,800$ units for $$5\mathrm{.}80$ each.

August $31$ Inventory on hand$-10,600$ 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$).$