A meat science researcher designed a study to investigate the impact of increasing the portion of grain (and hence decreasing the portion of hay) in the daily ration for cattle on the tenderness of beef steaks obtained from the cattle. Twelve steers of the same breed, age, and weight were selected for the study. Four of the steers were randomly assigned to one of the following three rations, factor A:
Ration 1: (A1) 75% grain, 25% hay
Ration 2: (A2) 50% grain, 50% hay
Ration 3: (A3) 25% grain, 75% hay
After being on the ration for 90 days, the steers were butchered, and four sirloin steaks were ­obtained from each carcass. The steaks were then randomly assigned to one of four aging times, factor B: 1, 7, 14, or 21 days. After being stored at 18C for 90 days, the steaks were thawed and then cooked to an internal temperature of 708C. Next, 68 cores (1.27 cm in diameter) were removed parallel to fiber orientation from each steak, and the peak shear force was measured on each core using a Warner€“Bratzler shearing device. The mean shear force values (kg) are given in the following table.

The treatment means are given in the following table.

a. Provide the linear model for this study. Include the ranges on all subscripts.
b. Provide a profile plot that will allow an assessment of the age by ration interaction.
c. Based on the table of means and your profile plot, does the decrease in mean shear force with increased aging of the steaks appear to be the same for all three rations?

Ration 1 Ration 2 Ration 3 Age 23 56 789 10 Mean 3.1 3.2 4.9 6.0 4.9 5.9 3.1 4.6 5.3 48 4.7 49 4.62 7 2.9 2. 4.1 5.2 5.2 58 2.8 4.4 5.2 4.6 4.5 4.8 4.30 14 24 2.5 34 5 44 5.1 3. 4.7 5.1 4.2 4.2 4.7 408 21 2.1 2.1 3.7 5.0 4.6 4.9 2.1 38 48 4. 3.8 4.4 3.78 Mean 3.61 4.34 4.63 Age Ration 1 14 2 Mean 4.30 358 335 323 361 4.63 455 .33 3.85 4.34 4.93 4.78 4.55 4.28 4.63 Mean 4.2 4.30 4.08 3.78