2. [12 points; allocated as specified below] Solve the following minimization problem: min{C = (x1 - 4)2 + (x2 - 4)2 s.t. 2x1 + 3x2 2 6, -3x1 - 2x2 2 -12, and x1, X2 2 0} X1,X2 a. [2 points] Write down the Lagrangian function. b. [4 points] Write down the Kuhn-Tucker conditions. c. [4 points] Find the optimum. Ensure that all the conditions set out are satisfied at this point, including that it is a minimum. d. [2 points] Is constraint qualification satisfied? Explain