Abstract:
Food security faces significant threats from climate change, population growth, and
economic pressures. Despite efforts to improve productivity, distribution, and sustainable
agriculture, many regions still remain insecure. Optimizing sweet potato yield requires
carefully designed experiments to identify key yield-enhancing factors. The main objective
of this study was to optimize sweet potato yield through advanced modelling with
augmented second order rotatable design using trigonometric functions. The specific
objectives were to: construct augmented second order rotatable designs in three
dimensions; determine optimality criteria D-, A-, T- and E- for augmented second order
rotatable designs; examine the relative efficiencies for augmented second order rotatable
designs and apply augmented second-order rotatable designs to obtain design points that
optimize sweet potato yield. The study transformed cyclic coordinates into Cartesian form
to create numerical sequences used in moment conditions for developing diverse sets,
which were further augmented to yield second-order rotatable designs in three-
dimensional space. The evaluation of each design's performance and its relative efficiency
involved the application of optimality criteria, such as D-, A-, T-, and E-criteria. The
augmented second-order rotatable design was fitted to the data to obtain design points
that optimize sweet potato yield. The R statistical software was used for modeling and
analysis while Python was used in the construction of the design and evaluation of
optimality criteria. The three augmented second order rotatable designs in three
dimensions were successfully constructed. Generally, the twenty three point second order
rotatable design turned out to be the most optimal and efficient design. Goat manure
significantly outperformed poultry and rabbit manure, quadratic effects and interactions
among poultry, rabbit, and goat manure also played a crucial role in boosting sweet potato
yield. The study found that the optimal levels of poultry manure, rabbit manure, and goat
manure that led to maximum yield were 35g/hole, 25g/hole and 45g/hole respectively.
The application of these specific quantities resulted in the highest yield performance of
4kg/mounding. In conclusion, the study developed an optimal and efficient augmented
second-order rotatable design. This advanced design was subsequently applied to
effectively optimize sweet potato yield, demonstrating its practical utility in enhancing
agricultural productivity. It is recommended that agricultural practitioners should consider
integrating goat manure into sweet potato farming practices to optimize yield. The study
underscores the importance of advanced experimental designs in agriculture for further
research, promoting more efficient and sustainable farming techniques.