Concord Distribution markets CDs of numerous performing artists. At the beginning of March, Concord had in beginning inventory $2,500$ CDs with a unit cost of $$7.$ During March, Concord made the following purchases of CDs$.$March $53,125$ @ $$8$March $215,750$ @ $$10$March $134,375$@ $$9$March $263,000$@ $$11$ during march $14,000$ units were sold. concord uses a periodic inventory system. 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.