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# Consider the following nonlinear programming problem. Maximize Z= 2x1 + 2x2 +4x3 - X3 . 2 subject to 2x1 +x2 +x3 5 4 and x1 20, x2 20, x3 2 0. (a)

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)

Consider the following nonlinear programming problem.
Maximize Z= 2x1 + 2x2 +4x3 - X3 .
2
subject to
2x1 +x2 +x3 5 4
and
x1 20, x2 20, x3 2 0.
(a)
Use the KKT conditions to determine whether (X], 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?

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