Myers Montgomery and AndersonCook 2009 describe a gasoline b

Myers, Montgomery and Anderson-Cook (2009)
describe a gasoline blending experiment involving three mixture
components. There are no constraints on the mixture proportions,
and the following 10-run design is used:
Design Point x1 x2 x3 y (mi/gal)
1 1 0 0 24.5, 25.1
2 0 1 0 24.8, 23.9
3 0 0 1 22.7, 23.6
4 0 25.1
5 0 24.3
6 0 23.5
7 24.8, 24.1
8 24.2
9 23.9
10 23.7
(a) What type of design did the experimenters use?
(b) Fit a quadratic mixture model to the data. Is this model
adequate?
(c) Plot the response surface contours. What blend would
you recommend to maximize the miles per gallon?

Solution