Central composite design (CCD) is widely applied in many elds to
construct a second-order response surface model with quantitative factors to
help to increase the precision of the estimated model. When an experiment
also includes qualitative factors, the e ects between the quantitative and
qualitative factors should be taken into consideration. In the present paper,
D-optimal designs are investigated for models where the qualitative factors
interact with, respectively, the linear e ects, or the linear e ects and 2-factor
interactions or quadratic e ects of the quantitative factors. It is shown that,
at each qualitative level, the corresponding D-optimal design also consists
of three portions as CCD, i.e. the cube design, the axial design and center
points, but with di erent weights. An example about a chemical study is
used to demonstrate how the D-optimal design obtained here may help to
design an experiment with both quantitative and qualitative factors more
eciently.