Perpetual Inventory Using LIFO

Beginning inventory, purchases, and sales for Item ER$27$ are as follows:

January $1$ Inventory $100$ units @ $$29$

$5$ Sale $80$ units

$11$ Purchase $111$ units @ $$33$

$21$ Sale $93$ units

Assuming a perpetual inventory system and using the last$-$in$,$ first$-$out $($LIFO$)$ method, determine $($a$)$ the cost of merchandise sold on January $21$ and $($b$)$ the inventory on January $31.$