Consider the following nonlinear programming problem. Maximize Z = 2x1^2 + 2x2 + 4x3 − x3^2 , subject to 2x1 + x2 + x3 <= 4 and x1 >= 0, x2 >= 0, x3 >= 0.

(a) Use the KKT conditions to determine whether (x1 , x2 , x3) = (1, 1, 1) can be optimal.

(b) If a specific solution satisfies the KKT conditions for this problem, can you draw the definite conclusion that this solution is optimal? Why?

(problem pictured below)

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