Problem 3 (28 points) Consider the following primal optimization problem where X and Y correspond to the two decision variables. X and Y are continuous decision variables. The primal problem is bounded and feasible. Primal Problem a. (3 points) Is the primal optimization problem in standard form (yes or no)? b. (10 points) Write down the dual of the primal optimization problem provided above. Use U,V, and W for the dual variables and clearly define the objective and constraints. The dual problem is bounded and feasible. (15 points) The optimal solution of the dual problem formulated in part (b) is U= 0.2,V=0.2, and W=0 i. ( 2 points) What is the value of the dual objective function at optimality? ii. (4 points) Which two constraints in the primal optimization problem are guaranteed to be satisfied with equality in the optimal solution? iii. (6 points) What is the optimal value of X and Y in the primal optimization problem WITHOUT using a computer solver (e.g., Excel)? There are still multiple approaches to this problem. iv. ( 3 points) What is the value of the primal objective function at optimality