$1.$ To produce cat foods, we need to order ingredient X from a global supplier. X is ordered in large barrels and is used at the rate of $1800$ barrels per year. Each order that is placed with the supplier costs $$50$ to process. Storage space is at a premium on the manufacturing floor and out in the yard, so their annual cost to hold inventory is $$82$ per barrel. Lead time is $6$ days.

$1$a$.$ What is the best order quantity?

$1$b$.$ What is the total cost $($including holding cost and ordering cost$)?$

$1$c$.$ What is the reorder point?