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A 19 pound rib-eye roast is a larger than average roast. I would suggest 15 to 20 minutes per pound at 350 degrees would be a good starting point but it really depends on how well done you want it to be. It is best to determine doneness by using a meat thermometer. Use the following guidelines for the different degrees of doneness: 140 degrees for rare, 145 degrees for medium rare, 160 degrees for medium, 165 degrees for medium well, and 170 degrees for well done. Keep in mind that it is recommended that beef be cooked to a minimum of 145 degrees for safety purposes so only cooking your roast to 140 degrees (rare) is not recommended.