Artificial Intelligence (AI) has evolved from a tool for automation to a powerful mechanism for rational decision support. AI is useful to generate mathematical insights for taking decisions that optimize strategic, operational and predictive outcomes. In this paper theoretical foundations and practical implementations of AI-driven decision systems is studied. It will also highlight connections between mathematical models and AI reasoning which will help in decision making across domains. Among the crucial mathematical fields that support AI for decision-making are linear programming, probability, game theory, graph theory and combinatorics. In this paper the study is concentrated on importance of linear programming problems in AI for decision making.