3.. A chemical engineer with a major oil refinery wanted to try a number of different additives to boost the 'octane level of the unleaded fuel produced at the refinery.

For the sake of secrecy his additives were uniquely coded: A,B, C, D, E. All additives were varied from their lowest to their highest.The engineer knew from prior experience that the following additives would interact with each other: AB, AE, BD, DE, CE, and AD. To make matters worse, his boss told him that if his experiment did not produce positive results, he could forget about any further raises. The engineer ran the following screening design:(Note: D = АС, Е = BC) (a) What is the defining relation? (b) Are any important interactions aliased with main effects? If you answer"yes", list the alias problems you found. (c) Generate a fold over of the design generated for this problem. (d) What is the defining relation for the fold over design? (e) Would a fold-over design salvage this experiment? (f) Should the engineer forget about his future raises?