Company Magenta has the following inventory history for the month of October.

$\backslash$table$[[$October $1,$Beginning Inventory,$65$ units,$$\frac{15\mathrm{.}50}{?}$ unit$],[$October $5,$Purchased units,$145$ units,$$\frac{16\mathrm{.}75}{?}$ unit$],[$October $27,$Purchased units,$80$ units,$$\frac{17\mathrm{.}50}{?}$ unit$]]$

The ending inventory on October ${31}^{st}$ is $60$ unity

Calculate the following for October using the different inventory costing methods:

$(1.)$ Last$-$In$,$ First$-$Out $($LIFO$)$

$($a$.)$ Cost of Inventory

$($b$)$ Cost of Goods Sold

$(2.)$ Average Cost

$($a$.)$ Cost of Inventory

$($b$.)$ Cost of Goods Sold