Aztec Products wishes to evaluate its cash conversion cycle $($CCC$).$ Research by one of the firm$$s financial analysts indicates that on average the firm holds items in inventory for $65$ days, pays its suppliers $35$ days after purchase, and collects its receivables after $55$ days. The firm$$s annual sales $($all on credit$)$ are about $$2\mathrm{.}1$ billion, its cost of goods sold represent about $67$ per cent of sales, and purchases represent about $40$ per cent of cost of goods sold. Assume a $365-$day year.

a$.$ What is Aztec Products$$ operating cycle $($OC$)$ and cash conversion cycle $($CCC$)?$

b$.$ How many dollars of resources does Aztec have invested in $(1)$ inventory, $(2)$ accounts receivable, $(3)$ accounts payable, and $(4)$ the total resources invested?

c$.$ If Aztec could shorten its cash conversion cycle by reducing its inventory holding period by $5$ days, what effect would it have on its total resource investment found in part B $(4)?$