Consider the following convex programming problem.
Maximize f(x) = 10×1 – 2×12 – x1 3 + 8×2 -x22
subject to
x1 + x2 ≤ 2
and
x1 ≥ 0, x2 ≥ 0.
(a) Use the KKT conditions to demonstrate that (x1, x2) = (1, 1) is not an optimal solution.
(b) Use the KKT conditions to derive an optimal solution.
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