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

August $1$

Inventory on hand$2,500$ units; cost $$6\mathrm{.}60$ each.

August $8$

Purchased $12,500$ units for $$6\mathrm{.}00$ each.

August $14$

Sold $10,000$ units for $$12\mathrm{.}50$ each.

August $18$

Purchased $7,500$ units for $$5\mathrm{.}20$ each.

August $25$

Sold $9,000$ units for $$11\mathrm{.}50$ each.

August $28$

Purchased $4,500$ units for $$5\mathrm{.}80$ each.

August $31$

Inventory on hand$8,000$ 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$).$