From a math perspective...
A competent maths person would understand that the cost per bed (at maximum occupancy) is indeed $450,000,000 divided by 3000 as that represents the cost per bed, not the cost per individual. They would also understand that cost per bed and cost per head are not the same thing.
So let's say you have $450 Million and 3,000 beds. During the course of a year that one bed was occupied by 10 different people.
So cost of one bend is $450/3000 = $150,000
Divided by 10 people - immigrants that rotate in and out - is $150,000 / 10 = 15,000 per head for that bed. This number will fluctuate wildly depending on that specific beds occupancy.
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From a logic perspective...
I'm not buying the $450 Million dollar per year premise.
To me that sounds like start-up costs where at least some portion is short term to get the facility up and running. A "one time" expense which has to account for procurement of trailers (I'm assuming those are mostly for office spaces, staff, cooking, medical, etc.) and the tents to house the prisoners. Then beyond materials acquisition you have to contractor costs to procure and setup the facilities and since it's being/been done at breakneck speeds there will be a premium associated with speed.
Short version is that in years 2 and 3 you will see the cost per bed significantly decrease.
WW