There is a geometric interpretation of the conditions an optimal solution must satisfy. If we graph Example 1.1.2, we get a picture like that in Figure 1.1.

**Figure 1.1:** Geometric interpretation

Now, examine the gradients of *f* and *g* at the optimum point. They
must point in the same direction, though they may have different
lengths. This implies:

which, along with the feasibility of , is exactly the condition of Case (ii).

Mon Aug 24 14:26:21 EDT 1998