DOES THAT ART HAVE PURPOSE

Recently,we have been talking about the difference between art and design .When I read more books or more sources,I confused more.Before I had been agreed with that art is concerned with pure aesthetics ,it is not utilitarian.But when I read the book "ART IS WORK",my idea has been changed .Just like the author said "art is work ","The overwhelming history of art ,in fact has been the history of people doing work for a specific purpose ,in other words ,commissioned works with specific intentions.(Milton Glaser)He also gave us some examples ,such as Michelangelo painted the "Last Judgement "not for himself ,not to express himself .His art work had its purpose.I totally agree with him.