Answer:
How much may Adrian deduct?
This depends on whether the museum is private or not. If the museum belongs to a public charity or a university, then Adrian can deduct full fair market value = $35,000. Since Adrian's AGI is $80,000, she could donate up to $40,000 (half her AGI).
But if the museum is a private organization, then Adrian can deduct only her basis in the vase = $15,000
How would your answer to Part a change if, instead of displaying the vase, the museum sold the vase to an antique dealer?
Once you donate artwork, unless you strict prohibit the museum from selling it, then they can sell it and you cannot do anything about it. Some donors specific certain terms for their donations, e.g. artwork cannot be sold and it must be exhibited at least a certain amount of time, in certain places, etc. But if Adrian didn't include any clause on her donation, then whatever happens to the vase is up to the museum.
Currently, museums are less likely to accept restricted donations, unless of course the artwork is worth it.
