Solution
= Solution
For a monarch point, $\widehat\xi_i=\max\{0,1-(\widehat\alpha+X_i^\top\widehat\beta)\}$. Point P2 lies well beyond the monarch-side dashed margin, so a plausible value is $0$. P1 lies between the decision boundary and that margin, so a plausible value is about $0.4$. P3 lies on the wrong side of the decision boundary, so its slack exceeds one; about $1.3$ is plausible. Points P1 and P3 are <support vectors>, while P2 is not.
Solved by gpt-5.6-sol high.