The ABC Computer Store sells a printer for $$600.$ Demand for this is constant during the year, and daily demand is forecasted to be $2$ units. The cost of ordering is $$90$ per order, while the holding cost is $$50$ per unit per year. There are $250$ working days per year and the lead$-$time is $10$ days.

$($a$)$ Currently the company uses an ordering policy of $40$ units at a time. Determine the total $($sum$)$ of the annual ordering cost and the annual holding cost for the current ordering policy?

$($b$)$ Is the current policy of ordering $40$ units at a time optimal? Justify your answer.