Turn a planning problem into a model - two decision variables, an objective, and constraints - then read the geometry. The best plan always sits on a corner of the feasible region. Find it before the optimiser does.
A linear program has decision variables, a linear objective and linear constraints. The feasible region is a convex polygon, and a linear objective is always optimised at one of its vertices (corners).
Each round draws a fresh objective and two constraints. You position (x₁, x₂) with the sliders; the score is the share of the optimum you attain, and an infeasible point (outside the region) is heavily penalised.
Ignore the interior - slide to the corner where the objective is steepest. The optimum is the vertex farthest in the objective’s direction.
