A mail$-$order firm processes $5,800$ cheques per day. Of these, $60$ percent are for $49$ and $40$ percent are for $84.$ The $49$ cheques are delayed two days on average; the $84$ cheques are delayed three days on average. Assume $30$ days in a month. a$.$ What is the average daily collection float? How do you interpret your answer? b$.$ What is the weighted average delay? Use the result to calculate the average daily float. c$.$ How much should the firm be willing to pay to eliminate the float? d$.$ If the interest rate is $7$ percent per year, calculate the daily cost of the float. e$.$ How much should the firm be willing to pay to reduce the weighted average float by $1\mathrm{.}5$ days?