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The value of a project to a client can be measured in part by the level of quality associated with the completed project. Quality is acknowledged to be an important component of project management, but its joint relationship with time and cost previously has not been modeled. This paper introduces the notion of a quality function for individual tasks and uses the functional form of the bivariate normal (after also evaluating a bivariate logistic form), to model quality at the task level. Using real data from two case studies, a translation agency and a software development company, the quality function is specified and incorporated into a mathematical programming model that allows quality to be explicitly considered in project planning and scheduling. An alternative model formulation leads to the creation of quality level curves that enable managers to evaluate the nonlinear tradeoffs between quality, time, and cost for each of the example projects. The results of these analyses lead to specific decisions about the planned values for these three fundamental dimensions at the task level and provide insights for project planning and scheduling that can be gained through improved understanding of the choices and tradeoffs.