Thesis (BS Applied Mathematics) -- University of the Philippines Mindanao, 2005

This study employed natural type of bicubic spline to model the response surface of glycerol wherein the second derivatives were equated to zero. Data sets was divided into subrectangles. To ensure continuity and smoothness, several conditions were imposed on the piecewise bicubic functions at every node of each subrectangle. These conditions were applied on the data sets of glycerol at two temperature levels (320C and 650C) obtained from a previous study. The amount of sodium hydroxide (NaOH) and methanol (MeOH) were the independent variables with the amount of glycerol as the dependent variable. A numerical constrained optimization was used to determine the maximum value of the bicubic function of each rectangular grid. The highest of all the maximum values gave the desirable combination of the amount of NaOH and MeOH that could generate the maximum amount of glycerol. The best combination was 1.08 grams of NaOH and 12.00 grams of MeOH at 320C. this could generate 135.17 grams of glycerol which is 119.53% of the input and a profit of PhP10.12. with these results, it is suggested that there should be an exploration on the area beyond 1.25 grams of NaOH and 12 grams of MeOH in both temperature levels. It is also recommended that another experiment be conducted to verify the actual amount of glycerol produced by the optimal combination.