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

August $1$ Inventory on hand$-2,600$ units; cost $$6\mathrm{.}70$ each.

August $8$ Purchased $13,000$ units for $$6\mathrm{.}10$ each.

August $14$ Sold $10,400$ units for $$12\mathrm{.}60$ each.

August $18$ Purchased $7,800$ units for $$5\mathrm{.}60$ each.

August $25$ Sold $9,400$ units for $$11\mathrm{.}60$ each.

August $28$ Purchased $4,600$ units for $$5\mathrm{.}80$ each.

August $31$ Inventory on hand$-8,200$ 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$).$

$\backslash$table$[[\backslash$table$[[$Perpetual LIFO:$],[$Beginning Inventory$]],$Cost of Goods Available for Sale,Cost of Goods Sold $-$ August $14,$Cost of Goods Sold $-$ August $25,\backslash$table$[[$Total Cost of$],[$Goods Sold$]],$Inventory Balance$],[\backslash$table$[[\backslash$table$[[$Number$],[$of units$]]],[2,600]],\backslash$table$[[\backslash$table$[[$Cost$],[$per$],[$unit$]]],[$$$6\mathrm{.}70$