What does this equation mean?

produces first-order conditions $\tfrac{1}{4}$(264+0.275y) = $\lambda$ = 0.275\,(296+$\tfrac{x}{4}$) , which reduce, after clearing terms, to a single tangency condition independent of the budget size: $y - x = 224$. The unconstrained-by-caps answer, in other words, wants Garchomp’s invested Speed to run 224 points ahead of its invested Attack — a gap wider than the entire 252-point ceiling on either stat individually. That single number is the whole explanation for why the observed spread looks like a blunt “max both” instinct rather than a delicate balance: a 224-point desired gap cannot fit inside a box only 252 points wide on a side, so the interior tangency point is infeasible, and because both partial derivatives stay strictly positive everywhere in the feasible region — 83.325 for Attack and 98.725 for Speed, evaluated at the corner itself — the true optimum is not a compromise but the corner: $x^\ast$ = $y^\ast$ = 252 , both stats pinned to their individual ceilings, precisely because the model would keep demanding more of each if the ceiling did not exist. That corner is the exact allocation Smogon’s Swords Dance spread uses, arrived at independently by a community of players optimizing by feel rather than by Lagrangian [ 7 ] .