Functions of Two or More Variables (with Constraint)
In the problem of finding an extreme value of a function f(x 1, x 2) of two variables, it may happen that the variables x 1 and x 2 are not independent but are connected by one or more relations called constraints. In theory, we can solve for one of the two variables in terms of the other, and proceed as in Chapter 1. In actual practice, however, we are held back by two considerations. First, it may be tedious to substitute one variable for another. Second, and more important, we have to be careful in choosing which one of x 1 and x 2 to be the independent variable. The following example illustrates the possible pitfalls when we are not careful.
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