Amanda Chen, the manager at a premier subscription firm, is tasked with optimizing marketing strategies to enhance customer acquisition and retention rates. The firm operates on a model that relies heavily on periodic subscriptions for a diverse range of products. In light of intensifying competition and evolving consumer preferences, the company recently rolled out an aggressive marketing campaign aimed at boosting subscription rates. The cornerstone of this initiative is a tailored one$-$time percentage discount offered to potential subscribers, hypothesizing that a financial incentive might sway their decision to subscribe.