Here is the original question that I submitted that I need help with comes from the book of Winston:

13.7-4. Consider the following quadratic programming problem: Maximize f(x) = 2x1 + 3x2 - x1 - X2 , 2 subject to and *1 20, X2 20. (a) Use the KKT conditions to derive an optimal solution directly.Consider the following quadratic programming problem: Maximize f(x) = 2X1 + 3X2 -X1^2 - X2^2 Subject to: X1 + X2 =0, X2>=0 Use the KKT (Karush-Kuhn-Tucker) conditions to derive an optimal solution directly.The Kuhn-Tucker Conditions The Kuhn-Tucker conditions are used to solve NLPs of the following type: max (or min) f (x] , X2 , ..., X,) s.t. 8 1 ( X , , X 2 , .. . , X n ) Sb, 82 ( X ] , X 2 , . .., X)