.

4. (30 points) mins.t.x15x2+3x12+2x22x1x24x1+5x2203x17x25x1,x20 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. c) Perform a single iteration of the modified simplex method to the problem formulated in part "b)". Write down the entering and leaving variables clearly. (Just one iteration!!!) 4. (30 points) mins.t.x15x2+3x12+2x22x1x24x1+5x2203x17x25x1,x20 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. c) Perform a single iteration of the modified simplex method to the problem formulated in part "b)". Write down the entering and leaving variables clearly. (Just one iteration!!!)