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Demand-side management (DSM) programs introduce complex pricing, requiring advanced control for cost minimization. Model Predictive Control (MPC) offers a solution but its performance hinges on appropriate hyperparameter tuning. We propose using Constrained Bayesian Optimization (CONFIG) to automate this process. In a case study, our optimized MPC reduced electricity costs by 26.90% compared to a rule-based controller and by 17.46% versus a manually tuned MPC. Analysis of real contracts further showed that optimal DSM program selection can lower monthly bills by up to 20.18%, demonstrating a data-driven path to significant consumer savings.