12. A study was conducted to nd the optimum ration of chloride and al-

kaline reserves (AR) in a product that was designed to add alkalinity to livestock rations. A small composite design was planned with the factors x1 = 1=

p chloride and x2 = ln(AR), but one combination of x1 and x2, had to be dropped from the study, and formulation problems with the other combinations resulted in an irregular design. Forty-eight cattle were blocked into 8 blocks based on initial weight and hip height. Three cattle had to be dropped from the study due to chronic health problems that were not related to the treatment. The goal was to nd the combination of x1 and x2 that resulted in the highest average daily gain in weight (ADG) over the course of the study. The data from the study are shown on the next page.

(a) Analyze the data with proc rsreg including dummy variables for the blocks, and check the assumptions of the tted model.

(b) Find the predicted maximum ADG.

(c) Import the data to SAS ADX and make a variance dispersion graph.

How far from rotatable is the irregular design?

(d) Make a contour plot to visually conrm the coordinates of your predicted optimum.