Answer:
Either is correct, but the particular choice will depend on the usage. Only one is correct for a given application. Let's look at a couple of examples and see how each is used.
"We are seeking a housekeeping supervisor, and any person with a year experience is encouraged to apply."
"We are seeking a housekeeping supervisor and all persons with a year of experience are encouraged to apply."
The examples are compound sentences, as you can see. The relative portion of the examples is the latter one, and here they are broken out:
"Any person with a year of experience is encouraged to apply."
"All persons with a year of experience are encouraged to apply."
In the examples, we see that "... person ... is..." and "... persons ... are ..." both meet the demands of proper English usage.