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

A bakery sells $2$;$000$ loaves of bread every month and orders our from a supplier. The annual carrying cost per unit flour $($one unit of our can be used to make one loaf of bread$)$ is $$8.$

Note: The following three questions are independent of each other.$$

$1.[3$ marks$]$ If the bakery orders $1$;$200$ units of flour each time, what is the length of each order cycle $($in month$)?$

$2.[4$ marks$]$ The bakery orders $1$;$800$ units of flour each time and finds that the annual inventory holding cost is twice the annual ordering cost. What is the fixed ordering cost?$$

$3.[4$ marks$]$ If$,$ instead, the optimal order size of flour is $2$;$400$ units, what is the fixed ordering cost?