Determine the ending inventory and 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. $($Round per unit cost to $3$ decimal places, eg$.15\mathrm{.}647$ and final answers to $0$ decimal places, e$.$g$.5,125.)$

Which cost flow method results in the lowest inventory amount for the balance sheet? The lowest cost of goods sold for the income statement?

$(1)$ results in the lowest inventory amount, $ $$

$(2)$ results in the lowest cost of goods sold, $