The Christie Corporation is trying to determine the effect of its inventory turnover ratio and days sales outstanding $($DSO$)$ on its cash flow cycle. Christies sales last year $($all on credit$)$ were $$150,000,$ and it earned a net profit of $6\%,$ or $$9,000.$ It turned over its inventory $7\mathrm{.}5$ times during the year, and its DSO was $36\mathrm{.}5$ days. Its annual cost of goods sold was $$121,667.$ The firm had fixed assets totaling $$35,000.$ Christies payables deferral period is $40$ days.a$.$ Calculate Christies cash conversion cycle.b$.$ Assuming Christie holds negligible amounts of cash and marketable securities$,$ calculate its total assets turnover and ROA.c$.$ Suppose Christies managers believe the annual inventory turnover can be raised to $9$ times without affecting sales. What would Christies cash conversion cycle, total assets turnover, and ROA have been if the inventory turnover had been $9$ for the year?