Option B is correct because the bank needs a SageMaker-supported algorithm and the resulting model must be explainable for regulators. AWS documentation states that the Amazon SageMaker AI linear learner algorithm is a built-in algorithm that provides a solution for classification and regression problems. Since determining whether customers qualify for a new product is a classification-style decision problem, linear learner fits the business requirement directly.

The explainability requirement strongly favors a simpler and more interpretable model family. AWS Prescriptive Guidance on model interpretability states that simple models are considered more interpretable because the effects of input features on the output are easier to understand. It specifically gives linear regression as an example where the magnitudes of coefficients provide a clear global feature-importance signal. While the question does not explicitly mention SageMaker Clarify, AWS documentation also says SageMaker offers explainability features to help interpret predictions, which complements inherently interpretable model types such as linear models.

The other options are weaker fits. Object2Vec is mainly for learning embeddings and similarity relationships rather than a straightforward explainable eligibility model. A neural network may work technically, but it is generally less interpretable for regulatory review. k-means is an unsupervised clustering algorithm and is not suitable for predicting whether a customer qualifies for a product. Because the bank wants a directly supported SageMaker algorithm and a model that is easier to explain to regulators, the best AWS-aligned answer is B, linear learner.