Sweet potato production has been faced with various constraints including small land sizes and inappropriate agronomic practices, especially on management of soil fertility. Many studies that have been carried out on the effects of application of farmyard manure on sweet potatoes yields have just been used to get the best treatment within the range of treatments used. However, the designs used in data analysis are not appropriate for optimisation process. Therefore, there is need to use an appropriate design that will optimise the yields within the limited available resources for sustainable production of sweet potatoes. The objective of this study was to determine the optimum operating settings and to optimise the yields and the yield components in sweet potatoes. The study was conducted at Chuka University horticultural demonstration farm. The experiment was laid out in a Randomised Complete Block Design and replicated three times. The treatments included cattle manure and poultry manure (0, 5, 10, 15 and 20 tons per hectare) and inorganic phosphate fertilizer (0, 20, 40, 60 and 80 tons of P2O5 per hectare). Data was collected on number of tubers, tuber diameter, length and weight of tubers per plot. Central Composite Design (CCD) was applied in the optimization process. Data obtained was analysed using R statistical software and the second order mathematical model which described the response as a function of input variables, was generated. The study found that the optimal levels of inorganic phosphate, poultry manure and cattle manure that led to maximum yield were; 2.895 tons/ ha, 7.5 tons/ ha and 14.88 tons/ha, respectively. The study demonstrated that CCD can serve as an inexpensive tool in optimization of the sweet potato yield. The study was also useful to the farmers in the area of study since they can get information on the optimal levels of application organic manure and phosphate fertilizer that would lead to maximum yields.