A coffee shop consumes on average $5000$ bags of 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

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

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

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

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

e$.$ The company currently carries a safety stock of $50$ bags. What is the annual cost to carry the safety stock of $50$ bags?the order is delivered $($i$.$e$.,$ cash on delivery$).$ There are no quantity discounts.

f$.$ The company currently carries a safety stock of $50$ bags. What is the reorder point?

g$.$ the coffee shop decided to switch its supply to a small coffee farm in South America. Due to the change of supply, the cost of ordering and receiving shipments is increased to $$26$ per order. All the other cost parameters remain the same. What quantity should the shop order with each order to the South American coffee farm?

h$.$ How much additional total annual cost of placing orders & carrying inventory $($cycle stock$)$ should the coffee shop pay if they switch to the South American coffee farm $($relative to the cost in part d$)?$