How much does it cost to construct a homeless shelter?

One inexpensive approach:

Procure some land outside the city limits and start a program. You could put in wooden floors and wooden sidewalks and pitch these tents. It's protection from wind, rain, sleet and snow and these people can officially claim an address. Work programs could be started whereby employers can pick up day labor from the available "pool" of workers. A 'Transition to Stability" program could propel these people into productive citizenry and permanent housing/employment.

I submit that there is no reason any human being should be without shelter and a clean place eat, shower and shave everyday and a place to wash their own clothes.

And there's not a city in this country that couldn't implement something like this within 6 months.