use Time::ParseDate;

# ...

# use some logic to find beginning of last week
# note: (localtime)[6] = wday (0-6) where 0 = Sunday
my($today) = (localtime)[6];
my($monday_lastw) = { # figure out days since monday of last week
   0  =>  6,
   1  =>  7,
   2  =>  8,
   3  =>  9,
   4  =>  10,
   5  =>  11,
   6  =>  12,
}->{ $today };
my($saturday_lastw) = $monday_lastw - 6; # (days since sat. of last wk)

# get unix timestamp of the date on /monday/ of last week
# (first second of last week)
push(@parms, (parsedate(qq{$monday_lastw days ago 00:00:00}))[0]);

# get unix timestamp of the date on /saturday/ of last week
# (last second of last week)
push(@parms, (parsedate(qq{$saturday_lastw days ago 23:59:59}))[0]);