Consider the situation described in Exercise 15.22. Rework this problem assuming that the model you want to fit is second-order and you can afford to perform 12 runs.

Data From Exercise 15.22

Suppose that you want to fit a first-order regression model with an interaction term to two continuous factors. You plan to conduct the experiment over the usual \(-1,+1\) region in both factors, but a physical constraint on the system limits the design region to \(x_{1}+x_{2} \geq 1.5\). You can afford to perform 10 runs.
a. Find a D-optimal design for this experiment.
b. Find an I-optimal design for this experiment.
c. Compare the two designs in terms of both the variance of the model regression coefficients and the variance of the predicted response.