There are $75$ units of the item in the physical inventory at December $31.$ The periodic inventory system is used. Determine the inventory cost using the $($a$)$ first$-$in$,$ first$-$out $($FIFO$)$ method; $($b$)$ last$-$in$,$ first$-$out $($LIFO$)$ method; and $($c$)$ weighted average cost method.