When a government officer needs to contract with the FOR PROFIT private sector to do work -- the government officer is incompetent.
With the military engineers, already being paid; and with the prison population as high as it is (all bit it presently mostly unjustified because of hoards of unconstitutional laws) there is absolutely no reason for government to contract with any private contractor -- except for corrupt and personal-gain reasons.
Private contracts almost always tend to mark up their products or services to get a standard 33%+ profit. When the government contracts with them, because of red-tape and regulation, they nearly always double the cost of the total project.
All things being equal, the government should be able to produce at least a good a quality as the private sector and at least as much as 50% less the cost -- because there is not supposed to be any financial profit in the calculations.