Solution
= Solution
The duplicated feasible set is the diamond $|\beta_1|+|\beta_2|\leq t$. A loss contour first touches an entire line segment of the diamond whenever the optimal total has the sign of a sloping face; all points on that segment give the same fit. As $t$ passes the unconstrained optimum, the solution set becomes the intersection of the interior diamond with the line $\beta_1+\beta_2=z/s$.