Betty bakes and sells bagels all year round. Betty has to plan and manage

inventories of paper take$-$out bags with her logo printed on them to satisfy customer demand.

Betty uses a total of $10,800$ take$-$out bags in a year. Betty$$s printer charges her $$10$ per order for

print setup independent of order size. Bags are printed at $5$ cents $($$$0\mathrm{.}05)$ each bag. It takes $4$ days

for an order to be printed and delivered. The annual inventory holding cost is $$0\mathrm{.}0125$ per bag.

Assume $360$ days per year.

$($i$)$ What is the optimal order quantity per order for Betty? $(3$ points$)$

$($ii$)$ How many times per year does Betty need to order? $(1$ point$)$

$($iii$)$ How many days will elapse between two consecutive orders? $(1$ point$)$

$($iv$)$ What is Betty$$s total annual cost of placing orders & holding inventory? $(2$ points$)$

$($v$)$ What is Betty$$s ROP if she keeps a safety stock of $50$ bags?