2. Quadratic optimality. Consider the following (Primal) quadratic program: minimize 2x2 + 3y' + 2ry -4x -by subject to rty>2 r + 2y = 3 a) Does strong duality hold? Why or why not? b) Write down the KKT conditions for this primal-dual pair of problems. c) Find the dual optimization problem corresponding to the primal problem above. Simplify your answer as much as possible. d) Solve the KKT conditions however you like to obtain a solution to both the primal and dual problems. e) Verify your work using JuMP. Specifically: . Solve the primal in JuMP to confirm your solution is correct . Find the optimal dual variables using the dual (. . .) command . Solve the dual you found in JuMP to confirm that its solution matches the solution found using the dual (. . .) command in the previous step. . Substitute the primal and dual solutions you found numerically into the KKT conditions to verify that they are satisfied. . Verify that strong duality holds