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

August $1$ Inventory on hand$2,100$ units; cost $$6\mathrm{.}20$ each.

August $8$ Purchased $10,500$ units for $$5\mathrm{.}60$ each.

August $14$ Sold $8,400$ units for $$12\mathrm{.}10$ each.

August $18$ Purchased $6,300$ units for $$5\mathrm{.}40$ each.

August $25$ Sold $7,400$ units for $$11\mathrm{.}10$ each.

August $28$ Purchased $4,100$ units for $$5\mathrm{.}80$ each.

August $31$ Inventory on hand$7,200$ 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$).$