Constraint and feasibility

Draws the hard limits as lines, so the space of plans that satisfy all of them at once becomes a visible region.

You have a budget in a spreadsheet, a savings goal on a sticky note, and a private rule that you will not become the friend who never comes out. Each one is a limit. Each one lives in a different place. So every month you pick a plan that satisfies whichever limit you happened to look at last, and then feel vaguely guilty about the other two.

Constraint and feasibility puts every hard limit on the same surface and shows you the region they leave. A constraint is a line you may not cross. Two constraints crossing carve a corner. Three or four carve a region, and that region is the set of plans that actually work. Everything outside it is not a bad option. It is not an option. The form's job is to make that distinction visible before you spend a month discovering it.

It has four common renderers. The feasible region draws limits as lines on two axes and shades what survives. The Pareto frontier plots options against two goals and traces the outer edge where improving one must cost the other. The trade-off curve is a single line for a single pair of goals, with the knee marked where the price of the next unit jumps. The constraint table is the same idea with no geometry: options as rows, limits as columns, and the one row that clears every column.

Use it when a decision keeps feeling impossible and you suspect that is because it is. The drawing either shows a region, in which case the problem is choosing within it, or it shows no region at all, in which case the constraints themselves have to move, and now you can see which one is cheapest to move. It is weak on anything soft. A preference is not a constraint, and drawing it as a line makes it lie.