Bailey Corporation is trying to determine the effects of its inventory turnover ratio and days sales outstanding $($DSO$)$ on its cash conversion cycle. Bailey's $2023$ sales $($all on credit$)$ were $$300,000,$ and it earned a net profit margin of $6\%,$ or $$18,000.$ It turned over its inventory four times during the year, and its DSO was $73$ days. The firm had fixed assets totaling $$70,000.$ Bailey's payables deferral period is $50$ days.a$.$ Calculate Bailey's cash conversion cycle.b$.$ Assuming Bailey holds negligible cash and marketable securities$,$ calculate its total assets turnover and ROA.c$.$ Suppose Bailey's managers believe that the inventory turnover can be raised to $6\mathrm{.}0$ times.What would Bailey's cash conversion cycle, total assets turnover, and ROA have been if the inventory turnover had been $6\mathrm{.}0$ for $2023?$