Get the needed equipment (hospital bed with a rail she can't clim over or through, a wheelchair, a walker, pottie chair, and a waist restraint you can attach to her normal sitting chair) and keep her at home. Just make sure that you don't use the waist restraint in a chair that she can tip over. (the wheelchair shouldn't be used as her normal sitting chair. it should be used only for transport, and only if needed.)
You can get good used hospital beds, wheelchairs and the like from places like Salvation Army, Goodwill, etc. Call around. If they don't have what you need, ask them if they know of an outlet in your town which sells used hospital beds or whatever else it is you need. If you keep searching, you will persevere. Those resources are always available, but are often under publicized. Also, look in the classified ads in the paper, look in your local greensheet or thrifty nickel (american classified ads is another name it has).
Enlist the help of relatives when you need a sitter. Or look for adult day care facilities (they have one in my small city).
When it (alzheimer's) advances, she will have to stop wearing dentures, and you will have to get a smoothie blender, and make smoothies for her to eat, as well as soup, and Ensure (a nutritious canned drink). You can feed that stuff to her with a turkey baster. Of course, you will need to put a bib on her to catch the spill.
You should keep her at home as long as you can, because in the later stages of the disease, she will forget how to swallow. This will necessitate the surgical installation of a stomach (feeding) tube. When she gets that, she may be better off in a professional care facility.
One day it will get to the point when she cannot be left alone in a room for any real amount of time, for safety reasons. When this happens, don't feel bad about putting a waist restraint on her so she can't get up from her chair during the times of the day when you can't watch her (when you wash dishes, or take a bath, etc.) I guarantee you, they do the same thing to folks in professional care facilities, even the best ones. But when they do it, they usually leave the people restrained for much longer than personal caregivers do. Just make sure that you don't use the waist restraint in a chair that she can tip over. Her normal sitting chair should be a heavy one she can't tip over.
We took care of my Grandmother at home for many years. She got much better care at home than she would have in any professional care facility.
Your cheapest option is to keep her at home. And as I say, you may have no choice but to put her in a professional care facility in a few years, so hang onto her as long as you can.
Good luck to you, and God bless you.