A mail$-$order firm processes $5,800$ checks per month. 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.

a$-1.$ What is the average daily collection float? $($Do not round intermediate calculations.$)$

a$-2.$ How do you interpret your answer? $($Do not round intermediate calculations.$)$

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.$)$

c$.$ How much should the firm be willing to pay to eliminate the float? $($Do not round intermediate calculations.$)$

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 to $1\mathrm{.}5$ days? $($Do not round intermediate calculations.$)$