Consider the following linearly constrained programming problem:

Minimize f(x)
x1 3  4x2 2  16x3, subject to x1  x2  x3
5 and x1 1, x2 1, x3 1.

(a) Convert this problem to an equivalent nonlinear programming problem that fits the form given at the beginning of the chapter (second paragraph), with m
2 and n
3.

(b) Use the form obtained in part

(a) to construct the KKT conditions for this problem.

(c) Use the KKT conditions to check whether (x1, x2, x3)
(2, 1, 2)

is optimal.