In its first month of operations, Crane Company made three purchases of merchandise in the following sequence: $(1)600$ units at $$5,$

$(2)650$ units at $$6,$ and $(3)750$ units at $$8.$ Crane uses a periodic inventory system.

$($a$1)$

Calculate weighted$-$average unit cost. $($Round answer to $3$ decimal places, e$.$g$.5\mathrm{.}125.)$

Weighted$-$average unit cost $