Being pedantic, linear programming relies on the fact that there is always one global optimum that occurs at a corner of the constraint simplex; in some circumstances there can be equal global optima not at a corner. But that's a minor quibble.

I was more commenting on the irony that my family choose dates that makes getting to them by public transport difficult rather than easy. Commuting day in,day out without using a car is a bigger change than what happens four or five exceptional days a year.

"Using a car less doesn't change the paradigm. Ditching the car does."

If your talking about the paradigm of Peak Oil, and your talking only about American cars, no, it doesn't.

RC

Linear programming tells us that the "solution" is never a compromise, but always an extreme. Switching paradigms is jumping to new maximum/minimum.

Having used linear programming as a tool professionally, three comments:

1. The intersections of the constraint planes (thinking of the problem geometrically) are indeed compromises. At the optimal solution, many different constraints may bind.
2. For a planner, learning which constraints are binding at the optimal solution is at least as valuable as the optimal variable values themselves because they suggest options for doing better, and
3. The space of potential solutions in the real world is seldom convex. In the LP world, there is always a path from where you are to where you want to be such that you are better off at each step. In the real world, not always true.