Rise and Shine has been buying cereal directly from the manufacturer for $$32$ per case. The company's annual demand for cereal is $275,000$ cases and the company believes that the demand is constant for each of the $250$ days per year that it is open for business. Average lead time from the supplier for new orders is a constant $5$ working days. The purchasing agent at Rise and Shine estimates the annual inventory carrying cost is $$3$ per case and it costs approximately $$55$ to prepare, send, and receive an order. Round calculations to at least $2$ decimal places.

a$)$ Based on the economic order quantity, how many cases of cereal should Rise and Shine order each time it places an order?

b$)$ What would the average annual inventory be based on the answer to $($a$)?$

c$)$ What is the reorder point based on the answer to $($a$)?$