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3600 pt * 5400 pt is equal to 15000 px * 22500 px which is what Illustrator is telling you and equal to 50 * 75 inches

Your artboard should be 3 * 4.5 inches

[ATTACH]71119[/ATTACH]

Here's an Illustrator file exported to PS with 1200 dpi 3 * 4.5 inches as you can see the image size is 3 * 4.5 inches

[ATTACH]71120[/ATTACH]

You can edit the artboard size by going here

[ATTACH]71121[/ATTACH]

Change the Width and Height

[ATTACH]71122[/ATTACH]