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 1 2

1 2 0 25.1 5 1 2 0 1 2 24.3 6 0 1 2

1 2 23.5 7 1 3

1 3

1 3 24.8, 24.1 8 2 3

1 6

1 6 24.2 9 1 6

2 3

1 6 23.9 10 1 6

1 6

2 3 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?