In its first month of operations, Wildhorse Company made three purchases of merchandise in the following sequence: $(1)350$ units at $$3,(2)400$ units at $$5,$ and $(3)500$ units at $$7.$ Wildhorse 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 $