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Implementation of software quality requirements is critical for producing high-quality softwares. High-level quality requirements are usually refined stepwise by different low-level quality requirements, until some potential functional design alternatives are identified. An important question is how design alternatives can be effectively selected to satisfice the quality requirements. This paper focuses on the satisficing statuses of nodes in the quality requirements goal tree models, and presents an automated reasoning technique to select design alternatives. The final satisficing status of quality requirements can be obtained provided that the satisficing statuses of design alternatives are assigned. Existing approaches propose reasoning approaches which do not support efficient identification if many design alternatives and candidate solutions may exist. Our work provides an alternative approach to identify what is the acceptable design decision in a timely manner. A case study is also presented to illustrate our proposed automated reasoning approach.