Turn the repulsion down

The barrier problem for the workshop, solved exactly at whatever mu you choose. The curve is where the answer goes as you sweep it.

Try this. Start at the far left, where profit is irrelevant and the point sits at the analytic centre. Drag towards zero and watch the receipt at the bottom: the promise shrinks in step with mu, and the real gap stays under it the whole way.

The promise is 5 mu at every setting, and the real gap sits under it at every setting. That is what a forecastable method looks like.