In this research study, Scheffe’s second degree polynomial based model was adapted for the optimization of the mechanical properties of a five component concrete. Here, rice husk ash which is derived from solid waste and contains high quantity of aluminosilicates which makes it a pozzolanic material is used as the fifth component in the concrete mixture. Applying Scheffe’s statistical simplex methodology, the mixture formulations; a total of ninety concrete cubes of 150 × 150 × 150 mm dimension were produced including the control points used for testing the adequacy of the model. The concrete sample were cured for 28 days before crushing test is carried out to obtain its compressive strength. The maximum compressive strength of 33.45 N/mm² was achieved with a corresponding mix ratio of 0.60:0.65:1.30:1.60:0.35 for fraction of water, cement, fine aggregate, coarse aggregate and rice husk ash respectively. The Scheffe’s model equation developed is \({\widehat{\mathrm{Y}}=24\mathrm{X}}_{1}+{27.35\mathrm{X}}_{2}+ {33.45\mathrm{X}}_{3}+21{\mathrm{X}}_{4}+ {16.95\mathrm{X}}_{5}+{23.3\mathrm{X}}_{1} {\mathrm{X}}_{2}+{1.1\mathrm{X}}_{1}{\mathrm{X}}_{3}+ {21.4\mathrm{X}}_{1}{\mathrm{X}}_{4}+ 22{.1\mathrm{X}}_{1}{\mathrm{X}}_{5}- 15{.4\mathrm{X}}_{2}{\mathrm{X}}_{3}+ {3.3\mathrm{X}}_{2}{\mathrm{X}}_{4}+ {5.4\mathrm{X}}_{2}{\mathrm{X}}_{5}- {16.9\mathrm{X}}_{3}{\mathrm{X}}_{4}-{23.8\mathrm{X}}_{3}{\mathrm{X}}_{5}- {3.9\mathrm{X}}_{4}{\mathrm{X}}_{5}\). The formulated mathematical model was validated and a suitable relationship was observed between the experimental and predicted values based on the outcomes of student t test and analysis of variance. The model can predict the compressive strength of rice husk ash blended cement concrete so as to inform early decision making when used as construction material.