obj.ttl derived?

[David Birdsong]

How is obj.ttl derived when both Expires and max-age is set by the backends?

We had a case where the backend was setting Expires to 60seconds after
the request and max-age was 5184000.  Additionally in vcl_fetch:

sub vcl_fetch {
        if (obj.ttl < 9000s) {
                set obj.ttl = 9000s;
        }
}

What would obj.ttl be set to given the Expires and max-age contradiction?