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

August $1$ Inventory on hand$-3,100$ units; cost $$7\mathrm{.}20$ each.

August $8$ Purchased $15,500$ units for $$6\mathrm{.}60$ each.

August $14$ Sold $12,400$ units for $$13\mathrm{.}10$ each.

August $18$ Purchased $9,300$ units for $$5\mathrm{.}80$ each.

August $25$ Sold $11,400$ units for $$12\mathrm{.}10$ each.

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

August $31$ Inventory on hand $-9,200$ 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$[[$Perpetual LIFO:,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$[[$Number of$],[$units$]],\backslash$table$[[$Cost$],[$per$],[$unit$]],\backslash$table$[[$Cost of Goods$],[$Avallable for Sale$]],\backslash$table$[[$Number of$],[$units sold$]],\backslash$table$[[$Cost$],[$per$],[$unit$]],\backslash$table$[[$Cost of Goods$],[$Sold$]],\backslash$table$[[$Number of$],[$units sold$]],\backslash$table$[[$Cost$],[$per$],[$unit$]],\backslash$table$[[$Cost of$],[$Goods Sold$]],\backslash$table$[[$Number of units in$],[$ending inventory$]],\backslash$table$[[$Cost$],[$per unit$]],\backslash$table$[[$Ending$],[$Inventory$]]],[\backslash$table$[[$Beginning$],[$Inventory$]],3,100,\backslash$table$[[$$