Please do and answer the follow questions

Problem 1 (35/100 marks). A full factorial design was used to identify the key variables affecting the separability of chalcopyrite (CuFeS2) and pyrite (FeS2) in a flotation circuit of a concentrator. The studied factors were: (1) pH, (2) froth depth, (3) superficial gas velocity, (4) solids flow rate and (5) collector concentration. Factor levels and codes are shown in Table 1.1. Results of the full factorial experimental design 25 are shown in Table 1.2. Table 1.1. Factor codes and levels of the 25 design Variable Symbol Level -1 +1 PH 8.5 9.5 Froth depth, m 0.5 0.75 Solids flow rate, tph 600 1200 Superficial gas velocity, cm/s 0.5 1.0 Collector concentration g/t 100 200 Perform the DOE analysis by using a DOE software (e.g. Minitab) for full factorial design. Based on the results, select the critical factors that should be considered for an optimization stage. Run a half fractional factorial design, quarter fractional factorial design (25-1 and 25-2, respectively) and a Plackett-Burman design for this system (hint: introduce the responses from the full factorial in Table 1.2, according to the selected design). Based on the results of each of these three DOE, select the factors would be considered for an optimization stage. Are there differences between and in comparison to the full factorial? Comment based on the results, exposing pros and cons of the full, fractional and Plackett-Burman designs as tools for the screening stage. And decide your final design and critical factors.Table 1.2. Results of the 23 factorial design Factor Result Run B C RCu-RFe, % A 63.00 56.24 45.52 41.01 65.15 54.18 41.16 36.31 65.01 GUDWN= JOANAUAWNE 56.53 44.33 38.67 64.16 55.71 39.68 35.70 66.90 17 18 57.48 44.03 19 20 +1 40.22 +1 59.46 54.28 22 +1 38.00 23 +1 24 +1 31.78 25 +1 61.75 59.08 26 +1 52.61 27 +1 28 +1 47.30 61.97 29 +1 56.33 30 +1 31 +1 45.51 41.36 32 +1