Solved: An article in Biotechnology Progress (2001, Vol. 17, pp. 366368) reported on an

Chapter 14, Problem 14-76

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An article in Biotechnology Progress (2001, Vol. 17, pp. 366368) reported on an experiment to investigate and optimize the operating conditions of the nisin extraction in aqueous two-phase systems (ATPS). A full factorial design 22 0.05. 0.5. with center points was used to verify the most significant factors affecting the nisin recovery. The factor was the concentration (% w/w) of PEG 4000 and was the concentration (% w/w) of Na2SO4. The range and levels of the variables investigated in this study are presented below. Nisin extraction is a ratio representing the concentration of nisin and this was the response y. Trial x1 x2 y 1 13 11 62.874 2 15 11 76.133 3 13 13 87.467 4 15 13 102.324 5 14 12 76.187 6 14 12 77.523 7 14 12 76.782 8 14 12 77.438 9 14 12 78.742 (a) Compute an ANOVA table for the effects and test for curvature with Is curvature important in this region of the factors? (b) Calculate residuals from the linear model and test for adequacy of your model. (c) In a new region of factor space a central composite design (CCD) was used to perform second order optimization. The results are shown in the following table. Fit a second order model to this data and make conclusions. 0.05. x2 x1 Coded Uncoded Trial x1 x2 x1 x2 y 1 1 1 15 14 102.015 2 1 1 16 14 106.868 3 1 1 15 16 108.13 4 1 1 16 16 110.176 5 1.414 0 14.793 15 105.236 6 1.414 0 16.207 15 110.289 7 0 1.414 15.5 13.586 103.999 8 0 1.414 15.5 16.414 110.171 9 0 0 15.5 15 108.044 10 0 0 15.5 15 109.098 11 0 0 15.5 15 107.824 12 0 0 15.5 15 108.978 13 0 0 15.5 15 109.169 14-77.