For a linear programming problem and its dual problem, label each of the following statements are true or false and justify your answers: a) The sum of constraints and variables are the same for both the primal and the dual problems. b) If the primal has an unbounded objective function, then the optimal value of the objective function of the dual problem must be zero. c) If the primal problem is feasible then the dual must also be feasible. d) If at the optimal solution x of a linear programming problem with constraints in canonical form Axb, a constraint i is satisfied as strict inequality, i.e., ai1x1+ai2x2++ainxn0. e) Changing the right-hand sides of a linear program that has an optimal solution may result to an unbounded problem. f) For linear programming problems with too many constraints compared to the number of decision variables, it is usually faster to solve the dual problem. g) The dual variables (shadow prices) indicate how the optimal value of the objective function changes with respect to changes in the values of the decision variables. h) The dual linear program is always easier to solve that the primal