No, it is no violation of non-profit standards for a not-for-profit to charge admission, or multiple admissions. Non-profits are not required to operate at a loss.  They are allowed to make money although it is very difficult for them to do so.

While you may be upset at the price, I am sure the $16 admission did not approach covering their cost of operating to support your visit.  It is stunning to calculate the cost of operating a museum on a per visitor basis.  A good book on this topic is "The Cost of Collecting" (hope that title is right.) It came out about 10 years ago.  At that time the cost per visitor came out to about $30. 

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