The structure and behaviour of organisms are moulded by two powerful optimizing processes: evolution and learning by trial and error. Evolution tends to maximize fitness; that is, roughly speaking, an organism's potential for passing its genes on to future generations. Animals may learn, for example, where to go and what to do to maximize food intake, and how to behave to maximize mating opportunity. The incentive to use optimization theory is not to prove that evolution or learning works, but to check our understanding. If my calculations tell me that a particular pattern of behaviour is the best one possible in given circumstances, and if real animals do something quite different, then that suggests that I may have failed to understand the issues in hand.
Often in optimization problems, there are limits to the ranges of values that variables can take. In the case of the jumping problem, there is a limit to the speed at which athletes can run. The model led to the conclusion that long jumpers should run up as fast as possible and set down the take-off leg at a steep angle, and that high jumpers should run up much more slowly and set down the leg at a shallower angle. The predicted speeds and angles agreed well with the speeds and angles that successful athletes actually use. The point of the exercise was not to discover the best way of jumping (it seems best to leave that to the athletes and their coaches), but to check that our understanding of muscle physiology is capable of explaining what athletes actually do.
