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Amazon maintains numerous distribution centers across the country, hoping to position stock as close as possible to demand in order to reduce response time. When customer orders are placed online, they can be shipped from the closest distribution center that has the item in stock. They use data to predict demand patterns for each center.

One item that currently has a consistent demand over the course of the year is Amazon Aware $100\%$ bamboo paper towels, $6$ pack.

Suppose demand at a given distribution center is $10,300$ per year. The cost for Amazon to place an order to replenish their stock of these is $$25.$ Holding cost is $$7$ per item per year. Assume a $365$ day year. Replenishment leadtime is $6$ days.

a$.$ Suppose Amazon wants to order twice a month, or $24$ times per year. How many would they order at a time? $($Round to integer$)$

b$.$ What would be the annual total inventory cost if they ordered twice a month?

c$.$ What would be the most economical order quantity $($EOQ$)$ for this item?

d$.$ What would be the annual total inventory cost if they used the EOQ?

e$.$ what would be the best reorder point to prevent stockouts and minimize cost if Amazon opted to maintain safety stock of $25$ packs.

f$.$ In the morning, they counted inventory to be $225.$ Throughout the day, they sold $25$ packs. Should Amazon place an order for replenishment given the best ROP found in the previous question?