A mail$-$order firm processes $5,800$ checks per day. Of these, $60$ percent are for $$49$ and $40$ percent are for $$84.$ The $$49$ checks are delayed two days on average; the $$84$ checks are delayed three days on average.$$Assume $30$ days in a month.

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a$-1.$What is the average daily collection float? $($Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.)$a$-2.$How do you interpret your answer?b$-1.$What is the weighted average delay? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$b$-2.$Calculate the average daily float. $($Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.)$c$.$How much should the firm be willing to pay to eliminate the float? $($Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.)$d$.$If the interest rate is $7$ percent per year, calculate the daily cost of the float. $($Use $365$ days a year. Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$e$.$How much should the firm be willing to pay to reduce the weighted average float by $1\mathrm{.}5$ days? $($Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.)$