QE2013_AC-3_ECE580-5

Part 1,2,3,4,5

Solution:

From the constraint, it can be seen that:

$ x_1 = x_3 = -x_2 $

Substitute into the objective function:

$ f(x) = x_2 (x_1 + x_3) = -2 x_2^2 $

Therefore it has a maximizer but no minimizer (f(x) goes to $ -\infty $ as $ |x_2| $ increases)

The maximizer is $ x_1 = x_2 = x_3 = 0 $. There f(x) reaches the maximum value of 0.

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