We consider decision problems that can be described by means of linear models. Depending upon how the objective functions(s) and constraints are treated, traditionally such models have been solved using linear programming, fuzzy linear programming, multiple objective linear programming or "what-if" -analysis. The use of these approaches is associated with a number of difficulties. We propose that an "evolutionary approach" be used to resolve such difficulties. In this approach, the decision-maker does not have to specify the model precisely prior to solving the problem. In fact, the model evolves progressively. A real-life application to a media selection problem is described.