Salamon Company had a beginning inventory on January $1$ of $160$ units of its product at a cost of $$20$ per unit.

During the year, the following purchases were made:

Mar. $15400$ units at $$23$

July $20,250$ units at $$24$

Sept. $4,330$ units at $$26$

Dec. $2100$ units at $$29$

$800$ units were sold. Salamon Company uses a periodic inventory system. Instructions:

a$.$ Determine the cost of goods available for sale.

b$.$ Determine $(1)$ the ending inventory, and $(2)$ the cost of goods sold under each of the assumed cost flow methods $($FIFO$,$ LIFO, and average$-$cost$).$ Prove the accuracy of the cost of goods sold under the FIFO and LIFO methodsV