Shown below is the activity for one of the products of Random Creations:

January $1$ balance, $80$ units @ $$50$ $$4,000$

Purchases:

January $18$: $40$ units @$\text{'}$$$51$

January $28$: $40$ units @ $$52$

Sales:

January $12$: $30$ units

January $22$: $30$ units

January $31$:$45$ units

Required:

Compute the January $31$ ending inventory and cost of goods sold for January, assuming Random Creations uses LIFO and a periodic inventory system.