Question: Problem 1 (40%). Consider the following convex programming problem: Maximize f(x) = 10x1 2x x} + 8x2 xz, subject to x1 + x2 0, x2

Problem 1 (40%). Consider the following convex

Problem 1 (40%). Consider the following convex programming problem: Maximize f(x) = 10x1 2x x} + 8x2 xz, subject to x1 + x2 0, x2 > 0. Write down the KKT conditions. (b) Use the KKT conditions to demonstrate that (x1, x2) = (1, 1) is not an optimal solution. Please show your steps. (c) Use the KKT conditions or a computer program to find the optimal solution

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