Big Poverty Pimpin'- Homeless Shelters & Schools

I'm going to quote the DCist post " Residents of D.C. General Homeless Shelter Complain of Difficulty Getting Out":

On a more immediate basis, Graham said that he'd like to see funding for the shelter increase; it currently costs $13.8 million a year to operate, and city officials say it costs $50,000 annually to shelter a family there. The larger issues of affordable housing and transitional programs also have to be addressed, he said, because without it homeless residents will continue returning to the shelter.

 $50K per family? Seriously? There is something not right with that number. Somebody is making a killing because that number points to some inefficiencies, and there is money to be made in someone's or some government's inefficiency. Or are the people who ran the school system before Fenty/Rhee in charge of the homeless shelters now?
Is the idea that if you spend a lot of money carelessly in the so called service in the "least of those", regardless of results, it is supposed to be right? It doesn't sound like the homeless families are being served well by the system.
I should say that I see sloppy inefficiency as a form of injustice, as a failure to use your G-d given talents with all your heart, soul, and brain in his service. It does a disservice to the poor.
I've finished former School Chancellor Michelle Rhee's book Radical. She makes a pretty good argument that poorly functioning schools do the poor a disservice, as education is a pathway out of poverty. DC was spending the most per student than most urban school systems and had horrible results and the money spent was wasted on a central bureaucracy that saw serving the students and teachers as a PITA, so did it poorly. She described a warehouse that had the equipment and supplies teachers needed, but the materials were not getting to the schools. The school system was spending the money but the results weren't being achieved.
In a post Fenty/Rhee DC school system the poor and the rest of the city is being better served. Families aren't automatically running to NoVa or Southern Maryland. There is lots of school choice. Our schools are way better, and they could be even better than now, and they are on the right track for becoming a school system that families want.
For $50K per family, which I must note is more than what the Help makes, DC can do better. I get that there is overhead, staff, electricity, stuff. But at that price homeless families should be getting a variety of services, which they aren't. In this case DC Homeless services is like a car with a messed up fuel line and money is gas. They need gas to go forward, but the gas is leaking or the line is clogged and putting more in the tank won't help matters.