Consider the quadratic programming example presented in Sec. 12.7.

(a) Use the test given in Appendix 2 to show that the objective function is strictly concave.

(b) Verify that the objective function is strictly concave by demonstrating that Q is a positive definite matrix; that is, xT Qx 0 for all x  0. (Hint: Reduce xT Qx to a sum of squares.)

(c) Show that x1
12, x2
9, and u1
3 satisfy the KKT conditions when they are written in the form given in Sec. 12.6.