You work for a steel company. The first step to recycling steel is to process scrap in an electric arc furnace (EAF) where scrap steel is melted for reprocessing. You know three factors affect the melt time of your scrap steel: the tap setting on the electrical transformer of the furnace {low or high), the pile from which you took the scrap steel for the batch (A or B), and the specific furnace you use (EAFl or EAFZ). The results of your experiments, reported in standard order, are shown below: _ __ __ _ 7 LOW B EAFZ 45 __ Calculate all the main effects, two factor interactions and three factor interactions by hand without using matrix algebra. Also build the linear model for the system by hand. Make sure to show all your work! [15 marks]