A manufacturer whose daily supply of raw materials is variable and limited can use the material to produce two different products in various proportions. The profit per unit of raw material obtained by producing each of the two products depends on the length of a product€™s manufacturing run and hence on the amount of raw material assigned to it. Other factors€” such as worker productivity, machine breakdown, and so on€” can affect the profit per unit as well, but their net effect on profit is random and uncontrollable. The manufacturer has conducted an experiment to investigate the effects of the level of supply of raw material, S, and the ratio of its assignment, R, to the two product manufacturing lines on the profit per unit of raw material. The ultimate goal is to be able to choose the best ratio, R, to match each day€™s supply of raw materials, S. The levels of supply of the raw material chosen for the experiment were 15, 18, and 21 tons. The levels of the ratio of allocation to the two product lines were 1 / 2, 1, and 2. The response was the profit ( in cents) per unit of raw material supply obtained from a single day€™s production. Three replications of each combination were conducted in a random sequence. The data for the 27 days are shown in the following table.

a. Draw conclusions from an analysis of variance table. Use α = .05.
b. Identify the two best combinations of R and S. Are these two combinations significantly different? Use a procedure that limits the error rate of all pairwise comparisons of combinations to be no more than 0.05.

Raw Material Supply (tons) Ratio of Raw Material Allocation (R) 1/2 15 18 21 22,20,21 21,20, 19 17 18, 16 21, 19.20 23,24, 22 21, 11.20 19, 18,20 20,19,21 20,22.24