In agricultural eld tests, two or more herbicides are often mixed together in so-called tank mixes in order to nd a mixture that is more eective than individual herbicides in controlling a multitude of pest weeds. In a specic test, various mixtures of x1: a herbicide formulated to control broad leaf weeds, x2: a herbicide formulated to control grass seedlings, and x3: a general-purpose herbicide were tested. The data from the tests are shown in Table 11.8. The response is the proportion of weeds controlled.

(a) Create the design shown in the table above using the SLD function in the mixexp package.

(b) Input the data and t the Schee special cubic model.

(c) Make a contour plot of your tted model and identify a mixture that would result in the highest % weed control.

(d) Transform the mixture components to independent factors and t the general quadratic model in the independent factors using R function lm.

(e) Make a contour plot in the independent factors as shown in the Appendix at the end of this chapter.

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Mixture Component % Weed Control Run x1 x2 x3 X1 Y 123 1 0 0 73 0 1 0 3 0 4 10 5 12 0 12 0 1 0 17 68 80 77 12 86 6 0 7 8 9 12 10 17 3 100 13 -100 -100 1100 100 100 3 110 12 92 75 93 88