You have conducted an experiment on a system with four process variables. Two of these factors are easy to control in the full-scale process (x1 and x2), and two of them are difficult to control (z1 and z2), and are regarded as noise factors. The variance of the noise factors is (see attachment) You have run an orthogonal first-order design, and after fitting the model you find that the mean square error from the ANOVA is 5 and the following model in the usual coded variables provides the best fit:

(see attachment)

a. From the above response model, find an expression for the response surface for the process mean.

b. From the response model, find a response surface model for the process variance.

c. Find the values of the controllable variables that minimize the transmitted variance.