Research suggests a T-Rex would need 50-100k kCal/day. Even if it ate a whole cow before starting, it would be hurting a week in.

Maybe it could survive the month, but would probably be severely malnourished at that point.

In any event, there is no mention of what happens if I fail to kill it. Does the experiment just end and I go home empty handed, or does the magic hut disappear and we fight it out to the death?