P$6\mathrm{.}2($LO $2),$ AP Mullins Distribution markets CDs of numerous performing artists. At the beginning of March, Mullins had in beginning inventory $2,500$ CDs with a unit cost of $$6\mathrm{.}50.$ During March, Mullins made the following purchases of CDs$.$

March $5$

$2,000$ @ $$8$

March $21$

$5,000$ @ $$10$

March $13$

$3,500$ @ $$9$

March $26$

$2,000$ @ $$11$

During March $12,000$ units were sold. Mullins uses a periodic inventory system.

Instructions

Determine the cost of goods available for sale.

Determine $(1)$ the ending inventory and $(2)$ the cost of goods sold under each of the assumed cost flow methods $($FIFO$,$ LIFO, and average$$cost$).$ Prove the accuracy of the cost of goods sold under the FIFO and LIFO methods. $($Note: For average$$cost$,$ round cost per unit to three decimal places.$)$

b$.$ Cost of goods sold:

FIFO

$$103,750$

LIFO

$$115,500$

Average

$$108,600$

Which cost flow method results in $(1)$ the highest inventory amount for the balance sheet and $(2)$ the highest cost of goods sold for the income statement?