I. Garrett Industries turns over its inventory six times each year; it has an average collection period of $45$ days and an average payment period of $30$ days. The firm's annual sales are $$3$ million. Assume there is no difference in the investment per dollar of sales in inventory, receivables, and payables, and assume a $365-$day year.

a$.$ Calculate the firm's cash conversion cycle, its daily cash operating expenditure, and the amount of resources needed to support its cash conversion cycle

b$.$ Find the firm's cash conversion cycle and resource investment requirement it is makes the following changes simultaneously.

Shortens the average age of inventory by $5$ days.

Speeds the collection of accounts receivable by an average of $10$ days.

Extends the average payment period by $10$ days.

c$.$ If the firm pays $13\%$ for its resources investment, by how much, if anything, could it increase its annual profit as a result of the changes in part b$?$

d$.$ If the annual cost of achieving the profit in part $c$ is $$35\mathrm{.}000,$ what action would you recommend to the firm? Why?