A small coffee shop consumes on average $5000$ bags of their most popular coffee beans each month. The shop pays $$13$ for each bag to the supplier. The cost of ordering and receiving shipments is $$16$ per order. Accounting estimates annual inventory carrying cost is $30\%$ of its value. The supplier lead time is a constant of $5$ operating days. The shop operates $240$ days per year, i$.$e$.,$ the shop operates $20$ days each month. Each order is received from the supplier in a single delivery. The coffee shop uses a continuous review $($i$.$e$.,$ fixed$-$order quantity$)$ inventory system and pays the supplier when the order is delivered $($i$.$e$.,$ cash on delivery$).$ There are no quantity discounts. Please keep two decimal places in your calculations.

$1.$ What quantity should the shop order with each order?

$2.$ How many times per year will the shop order on average?

$3.$ How many operating days will elapse on average between two consecutive orders?

$4.$ What is the store$$s minimum total annual cost of placing orders & carrying inventory $($cycle stock$)?$

$5.$ The company currently carries a safety stock of $50$ bags. What is the annual cost to carry the safety stock of $50$ bags?