The team urges purchasing an application that would significantly reduce work time and help meet the deadline, but it will increase project cost. The sponsor wants to consider a cheaper application that still saves time. What should the project manager do?

Creating a decision tree is the best approach because it provides a structured method to evaluate the different options (the team's preferred application vs. the sponsor's cheaper alternative) by quantifying potential outcomes, probabilities, and financial implications. This allows for an objective, data-driven decision that aligns with project objectives and stakeholder expectations. Raising a change request is premature; a decision needs to be made first. Purchasing the application without further analysis would be irresponsible, as it ignores the sponsor's input and the cost implications. Analyzing assumptions and constraints is part of a broader risk management process, but a decision tree is specifically designed for evaluating choices with uncertain outcomes and financial impacts, which is the core of this dilemma.