Making a hutch with an attached run will be more expensive than making just the hutch. Depending on what you are looking for, and the extent you want people to be able to do what you are proposing, it may be wise to not have a run at all. Ideal for the chickens? No, but hens have been dealing with worse for hundreds of years. (Battery hens.... shudder.... deal with much worse, and those are the eggs the low income population would be supporting anyhow.) A hutch is off the ground, has a seperate tray for removing the poo underneith, and sometimes even has two stories so that some hens are above and some are below. It can fit on your patio, like a rabbit hutch, and usually costs about $50 to build and $110 to buy.
You build a box out of plywood (one piece will do if you have the means to cut it into squares), add a chicken wire bottom (so the poo goes somewhere else) and a door in front and in back (to collect), then a secured closet rod roost. Then add 2X2's for legs, and a metal tray at the bottom to catch the poo that can be removed to be cleaned, and support pieces for the tray (which could easily be any scraps from the rest of the project cut to size). It's simple, cheap, and can fit on a patio. If kept clean, it doesn't smell, and you still get eggs.
It depends on what your end goal is for the project. It WOULD be good for the low income population to realise that taking care of your own critters for food is a plan for survival through hard times. When I was young, our chickens were often what kept us healthy due to our income and living conditions.
It also depends on your weather conditions though... what is your climate? Would this proposal come with lessons in chicken care or a booklet they could just throw away? If you are proposing these animals as pets, then I would require a short class on chicken care and maintence to get the funding for the project.
I have worked on a similar project here in Western WA with providing raised bed gardens for low income that wanted to grow their own food. It was a wonderful project that I wish I could have been a part of longer. I would imagine that between that project and this, we would loose a lot of the starvation via poverty in this country.
