•Fine aggregates were partially replaced by WFS and fly ash to synthesize GPC.•D-optimal mixture design of experiments was opted to formulate mixture compositions.•The empirical models for CS 7 and CS 28 were developed, verified, and validated.•RSM was applied to study the effects of mixture composition on compressive strength.•Optimization was performed to maximize the utilization of WFS and fly ash in GPC. This work examines the partial replacement of fine aggregates with waste foundry sand (WFS) and fly ash, process by-products, to synthesize geopolymer concrete (GPC). D-optimal mixture design of experiments was adopted to guide the proportion of mixture constituents (fine aggregates, WFS, and fly ash) to obtain desired responses (high compressive strengths). The experimentally measured responses/compressive strengths were successfully fitted to Scheffe polynomial model to obtain cubic models which represent compressive strengths of solidified GPC at 7th day curing time (CS 7) and at 28th day curing time (CS 28). The models were statistically evaluated by the standard error of design estimation and experimentally verified by comparing their predicted responses to the independently performed experiments. The models were subjected to analysis of variance (ANOVA) and residuals (diagnostics) for statistical significance and validation, respectively. The established models, hence obtained, were used to assess the impacts of relative proportions of mixture constituents at CS 7 and CS 28. It was observed that, although the highest compressive strength requires a high proportion of fine aggregates, yet, some mixture compositions could be proposed for better utilization of waste materials. Finally, the optimization was performed to maximize the usage of WFS and fly ash. A recipe was identified which yielded 18.9 N/mm² CS 7 and 22.3 N/mm² CS 28 by mere 32 wt. % contribution of fine aggregates in a (fine aggregates + WFS + fly ash) mixture. This study can be helpful in designing experiments and optimizing the utilization of similar waste materials into useful products.