Scenario: Calendar Kiosk must decide how many of next year's Nature Calendars to order by September. The calendars cost $$6\mathrm{.}50$ and are sold for $$12.$ Expected sales of the calendar based upon past years data is approximately $245$ calendars. Assume that demand can be approximated by a Poisson distribution. Order quantities are in units of $20($i$.$e$.$ there are $20$ calendars per box$).$ At the end of January, unsold boxes $($i$.$e$.$ unopened$)$ of calendars may be returned at the discounted refund of $$2$ per calendar $($$$40\mathrm{.}00$ per box$).$ To minimize the risk of stock$-$outs, Calendar Kiosk typically orders $280$ of the calendars each year. Ignore discounting.

If the goal of the kiosk is to maximize expected profit, determine the optimal order quantity $($remember that they can only order in quantities of $20).$