In answering the following questions, be sure that you clearly demonstrate your knowledge of the assumptions and procedures used to answer the questions. Present your analysis and interpretations carefully, completely, and concisely.

Your grade will be based on $($i$)$ how well you write your answer, $($ii$)$ how well you understand the problem, and $($iii$)$ how accurate your solution is$.$ CAUTION: COMPOUNDING OF ERRORS IS POSSIBLE.

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.

What quantity should the shop order with each order?

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

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

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

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

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