This paper focuses on prescriptive price optimization, which derives the optimal pricing strategy that maximizes future revenue or profit by using demand forecasting models for multiple products. Prescriptive price optimization requires accurate demand forecasting models because the accuracy of these models has a direct impact on pricing strategies aimed at increasing revenue or profit. However, existing methods have not been able to fully exploit them due to computational limitations. Therefore, the purpose of this paper is to establish a new prescriptive price optimization model that utilizes highly accurate demand forecasting models and can be solved exactly in realistic time. The prescriptive price optimization problem can be formulated as a mixed integer nonlinear optimization (MINLO) problem by using optimal regression trees as the demand forecasting model, which have a generalization performance as high as that of gradient boosting trees without losing interpretability. Although the MINLO problem is hard to solve, we reformulate it as a mixed integer linear optimization (MILO) problem by using exact linearization. This allows the problem to be solved exactly by an optimization solver. The effectiveness of our method is evaluated through simulation experiments by comparing with existing methods. Our simulation results demonstrate that our method improves the accuracy of demand forecasting and pricing strategies compared to existing methods.