The outdoor enthusiast turns its inventory $8$ times a year, has an average collection period of $57$ days, and has an average payment period of $30$ days. It has annual sales of $5$ million and cost of goods sold for $1\mathrm{.}8$ million assume $365$ days a year

$10$a$.$ What is the firm's operating cycle and conversion cycle?

$-10$b$.$ Using ratio efficiency, calculate the dollar value of inventory. Show calculations. $10$c$.$ Suppose the firm could reduce the average age of its inventory by $10$ days, form $45$ days to $35$ days by now how much would it reduce its dollar investment in working capital $($if you had no answer for $10b,$ using $250000)$