Multiple changes in cash conversion cycle Garrett Industries turns over its inventory $6$ times each year; it has an average collection period of $45$ days and an average payment period of $30$ days. The firm's annual operating$-$cycle investment is $$3$ million. Assume a $360-$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 if it makes the following changes simultaneously.

$(1)$ Shortens the average age of inventory by $5$ days.

$(2)$ Speeds the collection of accounts receivable by an average of $10$ days.

$(3)$ Extends the average payment period by $10$ days.

c$.$ If the firm pays $13\%$ for its resource 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 $$35,000,$ what action would you recommend to the firm? Why?