Problem 3. Write down the Kuhn-Tucker conditions for the following problems (simplify and give the final form): (a) Minimize 2 =-X, - X, - X+12(x + x} + X}) Subject to X1 + X2 + X3 31 7 4X1+2X2 5 X1, X2,X320 (b) Minimize Z = (X, -2X3)2 + 72(x} + X} + x3) Subject to X1 - X2 + X3 = 1 X1, X2, X3 20