3. Consider the following linearly constrained problem min: Z = x²-6x1+x³-3x2 s.t. x1 + x2 <1, x10, x2 0. (a) Obtain the KKT conditions for this problem. (b) Use the KKT conditions to check whether (x1, x2) = (0.5, 0.5) is an optimal solution. (c) Use the KKT conditions to derive an optimal solution.

Fig: 1