Camp Manufacturing turns over its inventory $5$ times each$$ year, has an average payment period of $38$days$,$ and has an average collection period of $69$ days. The firm has annual sales of $$$$3\mathrm{.}5$ million and cost of goods sold of $$$$2\mathrm{.}1$ million.$($Use a$365-$day year.$)$

a$.$Calculate the$$ firm's operating cycle and cash conversion cycle.

b$.$What is the dollar value of inventory held by the$$ firm?

c$.$If the firm could reduce the average age of its inventory from $73$ days to $63$days$,$ by how much would it reduce its dollar investment in working$$ capital?