Adventures in high theory - mystery solved

The correct analogy, I believe, is not to trees outside my window blocking the sun, but to grass on the golf course. The golf course manager needs to devote scarce mowing resources to trimming the grass on the greens and on the fairway. Each type of grass grows at different speeds. How much of his time should be devoted to the trimming of each type of grass, and what is the optimal height of each? Answer: on the saddle path, both types of grass are at their optimal height and the percentage of time devoted to cutting each type is constant. Off the saddle path, he devotes 100% of his time to the grass that is most in excess of its desired height. At least I think that's the meaning of this equation: