Question: Problem 2 (16 pts). Consider the following convex programming problem, where f(x) is known to be concave. maximize:f(x)=2x12x12+2x1x221x22+8x2subjectto:x1+2x28 where x10 and x20. 1. State the

Problem 2 (16 pts). Consider the following convex programming problem, where

Problem 2 (16 pts). Consider the following convex programming problem, where f(x) is known to be concave. maximize:f(x)=2x12x12+2x1x221x22+8x2subjectto:x1+2x28 where x10 and x20. 1. State the KKT conditions for above quadratic programming problem, and demonstrate that (x1,x2)= (1,1) is not optimal. 2. Use the modified simplex method to derive an optimal solution. (please indicate clearly the enter/leaving variable at each step)

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