(Solution) - Consider the quadratic programming example presented in Sec 13 7 a Use -(2025 Original AI-Free Solution)

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Consider the quadratic programming example presented in Sec. 13.7.
(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, xTQx 0 for all x 0.
(c) Show that x1 = 12, x2 = 9, and u1 = 3 satisfy the KKT conditions when they are written in the form given in Sec. 13.6.