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 $$10$ per book plus the cost of shipping the order. The shipping has a fixed cost of $$50$ per order and a variable cost of $$2$ per book shipped. So$,$ the cost for the books is $$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.