Try this example....the prison can detain 3000 immigrants at a time. The immigrants will be held for 30 days, one month....before catching a deportation flight.
So after one month those 3000 detainees are gone, and replaced with 3000 NEW detainee immigrants, who are there the next month....then they all catch a flight and their beds and cage goes to 3000 NEW migrant detainees.
This can happen 12 months, 12 times in a year.....so....12 x 3000= 36000 people in a year's time can be held there.
The cost to run the alligator Alcatraz is $450,000,000 (million) a year, divided by the 36000 immigrants that stayed there during the year is $12,500.
$450,000,000/36000=$12500 per head
If they go up in immigrants to the 5000 bed capacity as they plan, then that would be 60,000 migrants staying there during the 12 months....which would be even less of a per head cost if it stays at costing $450 million a year for the whole Alcatraz facility.