However, p-values indicated that inoculum rate of
T.harzianum (X2) and S.cerevisiae (X3) and aeration (X4) were not
significant factors whereas some of their interactions were significant,
thus removing nonsignificant factors from the model were
not hierarchical. Since, optimization of five factors would be very
difficult in practice, factors were evaluated by examining the variety
of graphs (Fig. 1) in order to find if some of them could be fixed
or not. Examining these graphs, it was observed that low inoculation rate of A.sojae led to higher bioethanol concentration
than high inoculation rate when the inoculation rates of T.harzianum
and S.cerevisiae were fixed at their low levels, agitation speed
was high and the vented flasks were used (Fig. 1a). Agitation speed
was an important factor for bioethanol production. The higher the
agitation speed the higher was the bioethanol production (Fig. 1b).