An answer of http://nabetani.sakura.ne.jp/hena/ord30taxi/

Solve.pm

use strict;
use warnings;
use Exporter qw(import);

our @EXPORT_OK = qw(solve);

my @fee_system = (
    [995, 400, 60],
    [845, 350, 50],
);

my %route = (
    AB => [1090, 0],
    BC => [960, 0],
    AC => [180, 0],
    CF => [200, 0],
    BG => [1270, 0],
    AD => [540, 1],
    CD => [400, 1],
    DF => [510, 1],
    DE => [720, 1],
    FG => [230, 1],
    EG => [1050, 1],
);

my %city = (
    A => 0,
    B => 0,
    C => 0,
    D => 1,
    E => 1,
    F => 1,
    G => 1,
);

sub _route ($$) {
    my $key = join '', sort @_;
    [@{$route{$key}}] or die "NO KEY $key";
}

sub solve ($) {
    my @order = split //, $_[0];
    my ($first_d, $first_f, undef) = @{$fee_system[$city{$order[0]}]};

    my @routes = map {
        [$order[$_], $order[$_ + 1], _route($order[$_], $order[$_ + 1])];
    } 0 .. $#order - 1;

    my $total_fee = 0;

    while (my $route = shift @routes) {
        my ($start, $end, $r) = @$route;
        my ($distance, $fee) = @$r;
        if ($first_d > $distance) {
            $first_d -= $distance;
        } elsif ($first_d == $distance) {
            warn "TODO 1";
            return 0;
            last;
        } else {
            $r->[0] -= $first_d;
            unshift @routes, $route;
            $total_fee += $first_f;
            last;
        }
    }

    if ($total_fee == 0) {
        return $first_f;
    }

    my $route;
    my $left_over = 0;
    while ($route = shift @routes) {
        my ($start, $end, $r) = @$route;
        my ($distance, $f) = @$r;
        my $fee = $fee_system[$f][2];

        # left_over
        if ($left_over > 0) {
            $distance -= 200;
            $distance += $left_over;
            $left_over = 0;
        }

        my $n = int($distance / 200);
        my $left = $distance % 200;

        $total_fee += $fee * $n;

        if ($left == 0) {
            warn "TODO 3";
        } else {
            $total_fee += $fee if $distance >= 0;
            $left_over = $left;
        }
    }

    return $total_fee;
}

1;

test.t

use strict;
use warnings;
use Solve qw(solve);
use Test::More;

while (<DATA>) {
    tr/\r\n//d;
    my ($no, $input, $output) = split /\t/, $_, 3;
    is solve $input, $output, "Test $no";
}

done_testing;

__DATA__
0	ADFC	510
1	CFDA	500
2	AB	460
3	BA	460
4	CD	400
5	DC	350
6	BG	520
7	GB	530
8	FDA	450
9	ADF	450
10	FDACB	750
11	BCADF	710
12	EDACB	800
13	BCADE	810
14	EGFCADE	920
15	EDACFGE	910
16	ABCDA	960
17	ADCBA	1000
18	BADCFGB	1180
19	BGFCDAB	1180
20	CDFC	460
21	CFDC	450
22	ABGEDA	1420
23	ADEGBA	1470
24	CFGB	640
25	BGFC	630
26	ABGEDFC	1480
27	CFDEGBA	1520
28	CDFGEDABG	1770
29	GBADEGFDC	1680