Acquiring information about uncertainty and updating belief before making the final decision are important steps in decision analysis. In this paper, a national laboratory (lab hereafter) uses decision analysis to choose the optimal project proposal for a public project submitted to the government. A project proposal consists of a system concept (system technology and specifications) and a budget. When choosing a project proposal, the lab may not know what might happen when the cost of the project exceeds the budget. If the cost only exceeds the budget for a small amount, the government may allow the project to continue. On the other hand, if the cost substantially exceeds the budget, the project may be cancelled. To assess this uncertainty, experts’ opinions are useful source of information. However, experts’ opinions may not always be available. This paper proposes a mathematical model to simulate the government’s actions and to update the lab’s belief about this uncertainty when experts’ opinions cannot be obtained. Information obtained from analyzing a mathematical model should help the lab update its belief and make better decisions.