Free Company's records show the following information related to one of its products: May $1$: Balance on Hand $-300$ units @ $$5\mathrm{.}00,$ May $12$: Purchased $600$ units @ $$6\mathrm{.}00,$ May $30$: Purchased $100$ units @ $$7\mathrm{.}00.$ Free uses a periodic inventory system. Assuming that $600$ units were sold during May. Copute the May $31$ inventory and cost of goods sold during May under each of the following methods: $1.$ FIFO, $2.$ LIFO, $3.$ Weighted average.