QUESTION # $2(10$ points$)$: Given the following OA$8$ and five factors A$,$B$,$C$,$D$,$ E with each has only two levels. a$.$ If only four factors A$,$ B$,$ C$,$ D$,$ are of interest, what column should be assigned for each of the four factors? b$.$ If the factor E is to be included, which columns should be assigned for E$?($Assume only AB interaction is significant$)$ c$.$ If two noise factors, N$1$ and N$2$ are used in the study, design the experiment layout using inner$-$array$/$outer$-$array format. d$.$ If the column $3$ is assigned for factor E$,$ what are the positive and$/$or negative impacts it may have in the study? Why?