The answer depends on the person's specific mental condition. Bear in mind that the person who has been diagnosed with Alzheimer's (or some other form of dementia), not you, must
be the one to finalize the document. There's a legal requirement that the person making a power of attorney must be "of sound mind." This mental competency requirement isn't too onerous to meet, but it can be elusive for some people suffering from dementia. To satisfy the standard, the person generally must be able to understand what a power of attorney is and does -- and must also be able to understand that he or she is making one.
If the person you're concerned about can't meet this standard, your best alternative is probably to secure a legal guardianship or conservatorship, which will enable you or another person to manage property and care concerns. This legal procedure takes more time and effort than a power of attorney, but many probate courts offer good self-help centers and can answer your questions. If this might be an option for you, consult your local probate court for more information. To find your local probate court, search online using probate and the name of your city or county.
For more on guardianships and conservatorships, see Conservatorship and Adult Guardianship: A Beginner's Guide.