solution :-

(a) LIFO Method

Under LIFO recent purchases are used for sales .

date of sale = 23rd january

so we can utilise 4 units from the purchase lot of jan 16, and 1 unit from the beginning inventory

Hence cost of goods sold = 4 * $ 210 + 1 * $ 180 = $ 1,020

In this case closing stock of five units contain 4 units from the purchase lot of jan 25 and 1 unit from the beginning inventory

so cost of inventory for five units = 1*$ 180 + 4*$ 215 = $ 1,040

(b) FIFO Method

Under FIFO method oldest stocks are used for sales.

so we can utilise 2 units from the beginning inventory and 2 units from the purchase lot of jan 16

hence, cost of goods sold = 2*$ 180 + 3*$ 210 = $ 780

in this case closing stock of 5 units containg 1 unit from the purchase lot of jan 16 and 4 units from the purchase lot of jan 25

so cost for 5 units of closing stock = 1*$210 + 4*$ 215 = $ 1,070

( c) Average cost method

In this method we use average cost for stocks

Total inventory in stock = 6 units

Purchase cost for these 6 units = $ 360+$ 840 = $ 1,200

Per unit average cost = $ 1,200 / 6 = $ 200

Cost of goods sold = 5 * $200 = $ 1,000

Closing inventory of stock contains 4 units from the recent purchase lot of jan 25 @ $ 215 per unit and one unit from the earlier inventory with an average cost of $ 200

Hence cost for 5 units of closing stock = $ 200 + $ 860 = $ 1,060

please find attachement.