Jillet Corporation began the year with inventory of $30,000$ units of its only product. The units cost $$8$ each. The company uses a perpetual inventory system and the FIFO cost method. The following transactions occurred during the year:

Purchased $150,000$ additional units at a cost of $$10$ per unit. Terms of the purchases were $210/,$ n$30/.$ The company uses the gross method to record purchase discounts. The inventory was purchased f$.$o$.$b$.$ shipping point and additional freight costs of $$0\mathrm{.}50$ per unit were charged to Jillet.

$3,000$ units purchased during the year were returned to suppliers for credit. Jillet was also given credit for the freight charges of $$0\mathrm{.}50$ per unit on the original purchase. The units were defective and were returned two days after they were received. The remaining inventory was paid within the discount period. $($Hint: The discount applies only to inventory and not the freight.$)$

Sales for the year totaled $145,000$ units at $$18$ per unit. $($Hint: The cost of the inventory sold includes the purchase cost of those units plus freight less purchase discount.$)$

On December $28,$ Jillet purchased $7,000$ additional units at $$10$ each. The goods were shipped f$.$o$.$b$.$ destination and arrived at Jillet$$s warehouse on January $4$ of the following year.

$32,000$ units were on hand at the end of the year.

Required:

$1)$ Determine ending inventory and cost of goods sold at the end of the year.

$2)$ Assuming that operating expenses other than those indicated in the above transactions amounted to $$190,000,$ determine income before income taxes for the year.

$3)$ For financial reporting purposes, the company uses LIFO $($amounts based on a periodic inventory system$).$ Record the year$-$end adjusting entry for the LIFO reserve, assuming the balance in the LIFO reserve at the beginning of the year is $$19,000.$

$4)$ Determine the amount the company would report as income before taxes for the year under LIFO. Operating expenses other than those indicated in the above transactions amounted to $$190,000.$