$!!!$#### A mail$-$order firm processes $4,500$ checks per month. Of these, $60$ percent are for $$35$

and $40$ percent are for $$67.$ The $$35$ checks are delayed two days on average; the $$67$

checks are delayed three days on average. Assume $30$ days per month.

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$.,32.)$