If you are running a designed experiment, the first thing you should do is use a screening design, Plackett Burman or DSD, to remove insignificant factors from your model and to help set the levels for each factor. Then you run an RSM on the factors that are left over.

For the calculations. you should use software. Anything less will take far too long to deal with by hand. I use Design Expert 9 software.   

Since the type of solvent is a qualitative variable and not a quantitative one, it could not be included in a RSM in a simple way. You can construct your CCD with the three quantitative variables petal mass, temperature and time of extraction (it is a total of 14 points + central point repetitions) and then carry these experiments with different type of solvent, and so you get a response surface for each solvent ...

Another option could be to use a mixture of two solvents in different ratios 4:0, 3:1, 2:2, 1:3 and 0:4, so you consider this ratio as a fourth quantitative variable in your CCD

Ok thanks Samer.....but you have mentioned about "it is a total of 14 points + central point repetitions" I didnt understand what exactly it is......sorry for my poor knowledge in  understanding this CCD and RSM....thanks....can u help me in understanding...in simple manner..

A CCD of k factors is formed by 2k factorial points (those have the coordinates +1 or -1), 2k star or axial points (those have one coordinate = +/- alpha and all other zeroes) and the central point (all coordinates are zeroes) repeated a number of times generally > 3

If you have 3 factors you will need 23=8 factorial points (8 vertices of a cube), 2×3=6 axial points (intersections of the 3 axes with the sphere going through the 8 vertices above) with alpha = sqrt(3). 8+6=14 and finally the central point (0,0,0) repeated at least 3 times (I suggest 6 times that you have a total of 20 experiment to carry out) 

Hi Samer,

Thanks for your contributions. I am specifically interested in this part of this thread:

" Since the type of solvent is a qualitative variable and not a quantitative one, it could not be included in a RSM in a simple way. You can construct your CCD with the three quantitative variables petal mass, temperature and time of extraction (it is a total of 14 points + central point repetitions) and then carry these experiments with different type of solvent, and so you get a response surface for each solvent ... "

I am going to do a central composite design optimization with three factors: two continuous and one categorical (with 2 levels). Minitab is giving me 26 runs and I think the design is exactly in line with what you said in this thread. Is there any book or published article supporting what you said? Or I wonder if there is a published research study having a similar design.

Minitab 17 is giving me the response optimization equation in two sub-equations each one related to the 2 levels of the categorical variable. Like this:

Categ. Var. High Y1= ……………………..

Low Y2 = …………………….

I am not sure if I am on the right way. A similar article can really help me or your and other friends’ ideas are appreciated.