Question $21$

A restaurant currently uses $62,500$ boxes of napkins each year at a constant rate over the $365$ days that it is open. The cost to order napkins is $$200$ per order and the annual carrying cost for one box of napkins is $$4\mathrm{.}00.$ If the orders are replenished at a rate of $500$ boxes per day, what is the new optimal order quantity? $($Hint: Non$-$instantaneous replenishment$)$

$7,500$ boxes.

$6,166$ boxes.

$5,000$ boxes.

$3,083$ boxes.