Large Language Models (LLMs) promise significant efficiency gains across information-intensive operations by automating repetitive language-based tasks. However, adoption decisions remain largely opportunistic, as organizations struggle to move from pilots to sustainable industrialization. Without systematic economic frameworks, practitioners cannot assess whether LLM investments create value in a given context. This paper develops a general economic model to support informed LLM adoption decisions in operational information systems. Facing high uncertainty, we represent parameters as random variables centered on authoritative benchmarks, and evaluate the model by Monte Carlo simulation across pessimistic-to-optimistic assumptions on LLM efficiency. The ROI distributions show the probability of profitability and the Value at Risk for each configuration, together with a sensitivity analysis of its main drivers. As a first instantiation, we apply the model to Security Operations Centers (SOCs), mapping workflows onto established standards to identify tasks suited to LLM augmentation. The model balances productivity gains, driven by alert volume, analyst effort, and LLM efficiency, against operational costs, including inference, infrastructure, and error remediation, covering both cloud API and self-hosted deployments. Results show that adoption economics are context-dependent, and that automation is an exploitable lever, gated by accuracy, while the cost of errors and the model's price are secondary. Across the analyzed models and prices, most configurations are unprofitable, with profitability limited to high-accuracy, low-uncertainty deployments. The model gives organizations a quantitative basis for evidence-based adoption decisions, by locating the boundary between profit and loss, and the loss risked beyond it.

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