Take a look at Datetime.

use DateTime;
my $dt = DateTime->last_day_of_month(
    year   => 2003,
    month  => 10,
    hour   => 1,
    minute => 30,
    second => 0,
);
print "Last day of month is " . $dt->day_name() . "\n";
[download]

This creates a new object that assumes that it is the last day of the month. Then you just call the day_name(), your done!