3. Consider the following quadratic programming problem: min -2x, – 2x2 + xỉ + 2x – 2x,x2 s.t. X1 +x2 < 3 2x1 + 3x2 2 6 X1,X2 2 0 a) Write down the KKT conditions. b) Suppose that this problem is to be solved by the modified simplex method. Formulate the linear programming problem (with artificial variables added if necessary) that is to be addressed explicitly. Identify the additional complementarity constraint that are enforced automatically by the algorithm.

6.2 9 please fill in A

The initial tableau of a linear programming problem is given. Use the simplex method to solve the problem. X2 X3 4 4 2 3 X₁ 1 4 3 -1 $₁ 1 0 0 $2 0 1 0 Z 0 0 1 16 60 The maximum is when x₁ = x₂ = x3 = . $₁=₁ and $2 = | (Type integers or simplified fractions.)

Linear Programming: I got started on it, please follow up with my solution or give a better one