Consider the following problem: Minimize (x1    3)^2 + (x2    2)^2 subject to x1^2    x2    3 $\le $ 0 x2    1 $\le $ 0    x1 $\le $ 0 Give the solution.
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['(0, 0)', '(2, 2)', '(3, 3)', '(2, 1)']
Figure 1 illustrates the feasible region. The problem, then, is to find the point in the feasible region with the smallest possible (x1    3)2 + (x2    2)2. Note that points (x1, x2) with (x1    3)2 + (x2    2)2 = c represent a circle with radius √c and center (3, 2). This circle is called the contour of the objective function having value c. Since one wishes to minimize c, one must find the circle with the smallest radius that intersects the feasible region. As shown in Figure 1, the smallest such circle has c = 2 and intersects the feasible region at the point (2, 1). Therefore, the optimal solution occurs at the point (2, 1) and has an objective value equal to 2. The approach used above to find an optimal solution by determining the objective contour with the smallest objective value that intersects the feasible region, is only suitable for small problems and is not practical for problems with more than two variables or those with complicated objective and constraint functions.