Melo et al. (2007) used a 24−1 factional factorial design with generator D = ABC to study the factors that in uence the production of levan by aerobic fermentation using the yeast Zymomonas mobilis. Levan is a sugar polymer of the fructan group, which has been shown to have anti-tumor activity against sarcoma and Ehrlich carcinoma in Swiss albino mice. The factors varied in the fermentation medium and their levels are shown in the table below.

(a) What is the dening relation and complete alias structure for this design?

(b) What is the resolution of this design?

(c) The fermentations were carried out batchwise in Pyrex asks. After 72 hours of fermentation, the levan produced was extracted from the fermented medium and its dry weight was determined. The results (in g.L−1) for the eight experiments (in standard order) were: 4.70, 14.67, 1.71, 3.73, 9.47, 7.61, 0.15, 4.78. From this data, calculate the seven eects and make a normal probability plot to determine what is signicant.

(d) Delete the smallest three eects and t the model again. Are the four eects left in the model signicant?

(e) Based on the eect heredity principle, what do you think the signicant string of aliased two-factor interactions could represent?

(f) Can the design be collapsed to a full factorial by ignoring insignicant factors?
(g) Based on what you said in

(e) write an interpretation of the signicant eects and interaction. Based on your model determine the factor levels that will produce the maximum dry weight of levan.

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Levels Label Factor - + A Sucrose initial concentration (g.L-1 150 250 B Temperature (C) 20 30 C Yeast extract initial concentration(g.L-) 2.0 5.0 D Agitation(rpm) 50 100