P$-$Generator is a manufacturer of industrial portable power generators. The finance manager is concerned about the firm's management of working capital.

a$)$ The average collection period and average payment period are $28$ days and $32$ days respectively. The firm turns over its inventory $10$ times each year $($assume $365$ days year$),$ and currently has annual sales of $$30$ million.

$($i$)$ Calculate the firm's operating cycle and cash conversion cycle, correct to $1$ decimal place.

$(5$ marks$)$

$($ii$)$ Determine the amount of resources needed to support the firm's cash conversion cycle.

$(4$ marks$)$

b$)$ P$-$Generator purchases $80000$ units per year of a component used in power generators production. The cost per order is $$40,$ while the carry cost is $$8$ per unit per year.

$($i$)$ Calculate the economic order quantity.

$(4$ marks$)$

$($ii$)$ Using your answer in $($i$),$ calculate the ordering cost, carrying cost and total inventory cost.

$(8$ marks$)$

c$)$ Suppose P$-$Generator operates a $250$ days per year, and maintains a minimum inventory level of $150$ units of safety stock. If the lead time to receive orders of the component is $5$ days, calculate the reorder point.

$(4$ marks$)$