Altira Corporation provides the following information related to its inventory during the month of August $2024$:August $1$Inventory on hand$3,400$ units; cost $$7\mathrm{.}50$ each.August $8$Purchased $17,000$ units for $$6\mathrm{.}90$ each.August $14$Sold $13,600$ units for $$13\mathrm{.}40$ each.August $18$Purchased $10,200$ units for $$6\mathrm{.}40$ each.August $25$Sold $12,600$ units for $$12\mathrm{.}40$ each.August $28$Purchased $5,400$ units for $$5\mathrm{.}80$ each.August $31$Inventory on hand$9,800$ 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$).$