8. Central composite design Consider using a central composite design for three factors, to include eight factorial points and six axial points.

(a) Determine the value of α to make the design rotatable.

(b) Investigate how α and the number of center points should be chosen to make the design both rotatable and orthogonal, if possible. If this is not possible, how can the design be made rotatable and nearly orthogonal?

(c) Investigate whether the design can be rotatable with orthogonal blocking. If not, then investigate whether orthogonal blocking is possible. If so, how many blocks could be used? Investigate whether orthogonal blocking and near rotatability is possible.