AQ$1.$ Inventory Management $(11$ marks$)$

A large law firm uses an average of $60$ boxes of copier paper a day. The firm operates $250$ days a year. It costs approximately $$450$ to order and receive a shipment of paper. Note: The following three questions are independent of each other.

$[3$ marks$]$ If the firm places $7\mathrm{.}5$ orders each year on average. What is the order size?

$[4$ marks$]$ If the optimal order size is $1,500$ boxes, what is the unit inventory carrying cost per year?

$[4$ marks$]$ If$,$ instead, the optimal total annual cost of inventory holding and ordering is $$10,000,$ what is the unit inventory carrying cost per year?