e that the easy changes are al- ready done and that any change we are contemplating is going to make something worse. As we consider changes that do something good and something bad, we have to con- sider the tradeoff between the good and the bad. We can think of the options available to us as some kind of geometric space called the feasible region. Figure 22.1 shows a two-dimensional picture, whereas reality often has dozens, hundreds, thousands, millions of variables. 5 Let us assume that both x and y in Fig. 22.1 are good things to increase. If we are currently at point P, then there are still changes to make that increase both x and y, so these are unambiguously good changes to make, easy decisions. Once we have exhausted the easy choices, we are at some point on the In mathematical calculation, we use the term closed form to mean an exact equation, or a spe- cific set of computations, used to obtain an answer. 4This statement may grate against the ears of two sets of readers: those who work in econom- ics and are familiar with opportunity costs and fans of Robert Heinlein, the science fiction author. For the economists, please note that we are taking opportunity cost into account. If we are in the planning stages, we can change our plans and find a system that will be better than the one we had previously planned at no greater cost. Even if systems already exist, we may find changes that are better in all ways. For example, replacing a defective component that has high maintenance cost with a reliable component may have a net dollar cost over time of less than zero, actually re- ducing total cost as well as increasing reliability. For Heinlein fans, the great author was correct when he gave us TANSTAAFL (there ain't no such thing as a free lunch). But some lunches pay for themselves. 'As an example of a large problem one of us (Rosenberg) has solved, think of an airline with 1500 flights and 100,000 possible passenger routings. For each routing and for each fare class (first class, full fare coach, two level