Demand for a book at Amazon is $250$ units per week $($assume $50$ weeks per year$).$ The book is supplied to Amazon from the book publisher for $$10$ per book plus the cost of shipping the order. The shipping cost has a fixed cost of $$50$ per order and a variable cost of $$2$ per book shipped. So$,$ the cost of the books is $$12$ per book, plus $$50$ times the number of orders placed.

Assume the annual inventory carrying cost is $20$ percent.

What is the annual holding cost per book?

Note: Round your answer to $2$ decimal places.

What is the optimal shipment size?

Note: Assuming $50$ weeks per year. Round your answer to the nearest whole number.

What is the average throughput time?

Note: Do not round intermediate calculations. Round your answer to $3$ decimal places.

Based on these data, calculate the economic order quantity and reorder point. Hint: Assume demand is deterministic.$$

Note: Round your answers to the nearest whole number.

The boss is concerned about this model because demand really varies. The standard deviation of demand was determined from a data sample to be $6\mathrm{.}15$ cans per day. The manager wants a $99\mathrm{.}5$ percent service probability. Determine a new inventory plan based on this information and the data in a$.$ Use Qopt from a$.$