This research investigated the optimization of locally sourced aggregate, mixed with variable cement ratios to determine its optimum compressive strength. Samples of standard sizes of local fine and coarse aggregate were obtained at the popular excavation sites. The concrete materials were weighed, batched, mixed, cast and cured using four different mix proportions of 1:2:4, 1.2:2:4, 1.4:2:4 and 1.6:2:4 of cement, fine and coarse aggregate at constant water/cement ratio of 0.5. A total of 48 concrete cubes of 150mmx150mmx150mm were produced, cured for 7, 14, 21 and 28 days and tested. Mathematical model equation relating the compressive strength of the local stone with variability of cement was developed using Response Surface Methodology (RSM). The significance and suitability of the equation was confirmed using the analysis of variance (ANOVA). The ANOVA for the quadratic and Surface Cubic model shows that the adjusted R2 of 0.9808 and F-value of 227.76 in compressive strength of the concrete is confidently accounted for by the independent variable. This demonstrates that the equation's predictions of compressive strength for various concrete structures are accurate. Therefore, utilization of local aggregate is advised for the construction of most of the dominant low-rise residential buildings in Anambra and other neighbouring States.