Pelham Inc. had no inventory as of August $1.$ It had the following transactions during August:

August $1$: purchased $2$ inventory items for $$4$ each

August $10$: purchased $3$ inventory items for $$3\mathrm{.}75$ each

August $15$: sold $1$ item for $$8$

August $20$ : purchased $3$ more inventory items for $$4\mathrm{.}25$ each.

August $25$ : sold $3$ items for $$8\mathrm{.}20$ each.

Assuming LIFO and a perpetual inventory system, what is ending inventory at August $31?$

$$15\mathrm{.}50$

$$16\mathrm{.}50$

$$32\mathrm{.}60$

$$32\mathrm{.}00$