This paper discusses the organization and the criterion for funding of an applied research project that can be regarded as a collection of necessary but potentially unsuccessful tasks. Each task might be successfully achieved by any of a number of alternative approaches. Each alternative approach can be regarded as a collection of necessary but potentially unsuccessful subtasks. Each subtask consists of subalternatives, etc. A comparatively simple procedure is given for selecting which projects to fund, for estimating various expected expenditures, and for determining that order of carrying out the tasks, alternatives, subtasks, etc., of a project that minimizes the project's expected cost. The procedure takes into account the possibility that the project may fail and be abandoned before all tasks, subtasks, etc., are performed and the possibility that engineering considerations may exclude some economically desirable task orderings. A number of industrial practices are discussed from this viewpoint.