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

August $1$ Inventory on hand$4,800$ units; cost $$6\mathrm{.}70$ each.

August $8$ Purchased $19,200$ units for $$6\mathrm{.}90$ each.

August $14$ Sold $14,400$ units for $$13\mathrm{.}40$ each.

August $18$ Purchased $14,400$ units for $$7\mathrm{.}00$ each.

August $25$ Sold $16,800$ units for $$12\mathrm{.}40$ each.

August $28$ Purchased $9,600$ units for $$7\mathrm{.}20$ each.

August $31$ Inventory on hand$16,800$ units.

Required:

Using calculations based on a periodic 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 each of the following cost flow methods $($FIFO$,$ LIFO, Average Cost$)$