4 Suppose an NLP appears to be separable except for the fact that a term of the form xixj appears in the objective function or constraints. Show that an NLP of this type can be made into a separable programming problem by defining two new variables yi and yj by xi

1 2

(yi yj) and xj

1 2

(yi yj). Use this technique to transform the following NLP into a separable programming problem:

max z = x + 3xx2-x s.t. xx4 x + x2 6 xX1X20