Consider the following linear programming problem U V Max 5X + 3Y+ 22 s.t. X + 2Y+ 3Z X Y 2X + Y 5Z X Y Z 2 W VI VI VI Al Al Al 20 14 70 0 0 0 The problem is already in standard form and we are showing the dual variables associated with each constraint in red beside the constraints. a) Write out the dual objective function. Be sure to state whether it is a minimization or a maximization. b) Write out the dual constraints. Also, clearly indicate and conditions on the dual variables. c) Consider the following possible primal/dual solutions to the problem: w X 17 Y 0 Solution 1 2 3 4 z 1 0 16 2 U V 1.55 4 2.66666667 2.33333333 2 4 1.5 0 0 0 0 1 15 19 3 1 1 1 Only one of these solutions is optimal? Which one is it? Hint: an optimal solution must satisfy the following conditions: All primal constraints must be satisfied All dual constraints must be satisfied The primal and dual objective functions must be equal d) For each solution that cannot be the optimal solution, give at least one reason why that solution cannot be the optimal solution