Simplex Pivoter

How to play

The tableau

Variables across the top are the independent (nonbasic) variables and are all zero, so the basic solution reads straight off the constant column. Variables down the left are dependent (basic). The x variables are the decision variables and the t variables are the slacks; both move between the top and the side as you pivot, and the panel under the tableau always shows all of them.

Pivoting

Tap a nonzero entry in a constraint row. Its row label and column label trade places and the tableau is rewritten so that every row still expresses its left label in terms of the new top labels.

Calling it

Exactly one of three things is true of every puzzle, each with probability one third:

• Basic solution is optimal — call it and the game shows you the optimal values of the decision variables, the slacks there, and the maximum of f.
• Feasible region is empty — some constraint row rules out every nonnegative point.
• Objective is unbounded above — from a feasible tableau, some direction raises f forever.

A call is only accepted when the tableau you are looking at certifies it — a feasible constant column with no positive entry left in the objective row, a row that rules out every nonnegative point, or a column that raises f forever. Naming the right outcome from a tableau that does not yet show it is still a miss, so you have to pivot until the answer is visible rather than guess it. Pivots and misses are both recorded, so the daily challenge rewards getting there in few pivots with no wrong calls. Par is how many pivots the textbook algorithm needs.

Reading off the answer

Got it