Charming Paper Company sells to the $12$ accounts listed here.

Capital Financial Corporation will lend $90$ percent against account balances that have averaged $30$ days or less, $80$ percent for

account balances between $31$ and $40$ days, and $70$ percent for account balances between $41$ and $45$ days. Customers that take over

$45$ days to pay their bills are not considered acceptable accounts for a loan.

The current prime rate is $15\mathrm{.}5$ percent, and Capital charges $4\mathrm{.}5$ percent over prime to Charming as its annual loan rate.

a$.$ Determine the maximum loan for which Charming Paper Company could qualify.