A mail$-$order firm processes $5,300$ cheques per month. Of these, $60$ percent are for $$55$ and $40$ percent are

for $$80.$ The $$55$ cheques are delayed two days on average; the $$80$ cheques are delayed three days on

average.

a$.$ What is the average daily collection float? How do you interpret your answer?

b$.$ What is the 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 $($compounded daily$),$ calculate the daily cost of the float.

e$.$ How much should the firm be willing to pay to reduce the weighted average float to $1\mathrm{.}5$ days? $($i$.$e

the new desired weighted average float is $1\mathrm{.}5$ days$).$