Consider an experiment with 5 input variables. (i) Obtain an appropriate 1/2 fraction of the 25 factorial to fit a first-order model. (ii) For the design chosen in (i) sketch the ANOVA table assuming that each design point is replicated twice. (iii) Suppose we need to run the experiment in blocks of size 8. Write out an appropriate plan, give the associated linear model and outline the ANOVA table.