A local hardware shop is open $200$ days a year and sells $20$ units of one cordless drill every day. Each drill costs $$10$ with an annual holding cost of $20\%$ of the purchase cost. It costs the shop $$10$ to place an order, and it always takes $4$ days to receive an order.

Please note computational steps are optional for possible partial credit.

$($a$)$ To minimize the total annual costs, how many drills should the shop order each time $($rounding to the nearest integer if necessary$)?$

Answer: $q,$

$($b$)$ What is the appropriate reorder point $($rounding to the nearest integer if necessary$)?$

Answer:

$($c$)$ If the annual holding cost of one unit of drill drops to $5\%$ of the purchase price, while everything else remains the same, the new economic order quantity will become $q,($fill in percentage, e$.$g$.,10\%,120\%)$ of the original optimal order quantity.